Daily Papers

Camera-controllable image editing aims to synthesize novel views of a given scene under varying camera poses while strictly preserving cross-view geometric consistency. However, existing methods typically rely on fragmented geometric guidance, such as only injecting point clouds at the representation level despite models containing multiple levels, and are mainly based on image diffusion models that operate on discrete view mappings. These two limitations jointly lead to geometric drift and structural degradation under continuous camera motion. We observe that while leveraging video models provides continuous viewpoint priors for camera-controllable image editing, they still struggle to form stable geometric understanding if geometric guidance remains fragmented. To systematically address this, we inject unified geometric guidance across three levels that jointly determine the generative output: representation, architecture, and loss function. To this end, we propose UniGeo, a novel camera-controllable editing framework. Specifically, at the representation level, UniGeo incorporates a frame-decoupled geometric reference injection mechanism to provide robust cross-view geometry context. At the architecture level, it introduces geometric anchor attention to align multi-view features. At the loss function level, it proposes a trajectory-endpoint geometric supervision strategy to explicitly reinforce the structural fidelity of target views. Comprehensive experiments across multiple public benchmarks, encompassing both extensive and limited camera motion settings, demonstrate that UniGeo significantly outperforms existing methods in both visual quality and geometric consistency.

Predictive world models that simulate future observations under explicit camera control are fundamental to interactive AI. Despite rapid advances, current systems lack spatial persistence: they fail to maintain stable scene structures over long trajectories, frequently hallucinating details when cameras revisit previously observed locations. We identify that this geometric drift stems from reliance on screen-space positional embeddings, which conflict with the projective geometry required for 3D consistency. We introduce ViewRope, a geometry-aware encoding that injects camera-ray directions directly into video transformer self-attention layers. By parameterizing attention with relative ray geometry rather than pixel locality, ViewRope provides a model-native inductive bias for retrieving 3D-consistent content across temporal gaps. We further propose Geometry-Aware Frame-Sparse Attention, which exploits these geometric cues to selectively attend to relevant historical frames, improving efficiency without sacrificing memory consistency. We also present ViewBench, a diagnostic suite measuring loop-closure fidelity and geometric drift. Our results demonstrate that ViewRope substantially improves long-term consistency while reducing computational costs.

Urban scene reconstruction requires modeling both static infrastructure and dynamic elements while supporting diverse environmental conditions. We present StyledStreets, a multi-style street simulator that achieves instruction-driven scene editing with guaranteed spatial and temporal consistency. Building on a state-of-the-art Gaussian Splatting framework for street scenarios enhanced by our proposed pose optimization and multi-view training, our method enables photorealistic style transfers across seasons, weather conditions, and camera setups through three key innovations: First, a hybrid embedding scheme disentangles persistent scene geometry from transient style attributes, allowing realistic environmental edits while preserving structural integrity. Second, uncertainty-aware rendering mitigates supervision noise from diffusion priors, enabling robust training across extreme style variations. Third, a unified parametric model prevents geometric drift through regularized updates, maintaining multi-view consistency across seven vehicle-mounted cameras. Our framework preserves the original scene's motion patterns and geometric relationships. Qualitative results demonstrate plausible transitions between diverse conditions (snow, sandstorm, night), while quantitative evaluations show state-of-the-art geometric accuracy under style transfers. The approach establishes new capabilities for urban simulation, with applications in autonomous vehicle testing and augmented reality systems requiring reliable environmental consistency. Codes will be publicly available upon publication.

Reconstructing dense geometry for dynamic scenes from a monocular video is a critical yet challenging task. Recent memory-based methods enable efficient online reconstruction, but they fundamentally suffer from a Memory Demand Dilemma: The memory representation faces an inherent conflict between the long-term stability required for static structures and the rapid, high-fidelity detail retention needed for dynamic motion. This conflict forces existing methods into a compromise, leading to either geometric drift in static structures or blurred, inaccurate reconstructions of dynamic objects. To address this dilemma, we propose Mem4D, a novel framework that decouples the modeling of static geometry and dynamic motion. Guided by this insight, we design a dual-memory architecture: 1) The Transient Dynamics Memory (TDM) focuses on capturing high-frequency motion details from recent frames, enabling accurate and fine-grained modeling of dynamic content; 2) The Persistent Structure Memory (PSM) compresses and preserves long-term spatial information, ensuring global consistency and drift-free reconstruction for static elements. By alternating queries to these specialized memories, Mem4D simultaneously maintains static geometry with global consistency and reconstructs dynamic elements with high fidelity. Experiments on challenging benchmarks demonstrate that our method achieves state-of-the-art or competitive performance while maintaining high efficiency. Codes will be publicly available.

Reconstructing 3D geometry from streaming video requires continuous inference under bounded resources. Recent geometric foundation models achieve impressive reconstruction quality through all-to-all attention, yet their quadratic cost confines them to short, offline sequences. Causal-attention variants such as StreamVGGT enable single-pass streaming but accumulate an ever-growing KV cache, exhausting GPU memory within hundreds of frames and precluding the long-horizon deployment that motivates streaming inference in the first place. We present OVGGT, a training-free framework that bounds both memory and compute to a fixed budget regardless of sequence length. Our approach combines Self-Selective Caching, which leverages FFN residual magnitudes to compress the KV cache while remaining fully compatible with FlashAttention, with Dynamic Anchor Protection, which shields coordinate-critical tokens from eviction to suppress geometric drift over extended trajectories. Extensive experiments on indoor, outdoor, and ultra-long sequence benchmarks demonstrate that OVGGT processes arbitrarily long videos within a constant VRAM envelope while achieving state-of-the-art 3D geometric accuracy.

Image-to-Video generation (I2V) animates a static image into a temporally coherent video sequence following textual instructions, yet preserving fine-grained object identity under changing viewpoints remains a persistent challenge. Unlike text-to-video models, existing I2V pipelines often suffer from appearance drift and geometric distortion, artifacts we attribute to the sparsity of single-view 2D observations and weak cross-modal alignment. Here we address this problem from both data and model perspectives. First, we curate ConsIDVid, a large-scale object-centric dataset built with a scalable pipeline for high-quality, temporally aligned videos, and establish ConsIDVid-Bench, where we present a novel benchmarking and evaluation framework for multi-view consistency using metrics sensitive to subtle geometric and appearance deviations. We further propose ConsID-Gen, a view-assisted I2V generation framework that augments the first frame with unposed auxiliary views and fuses semantic and structural cues via a dual-stream visual-geometric encoder as well as a text-visual connector, yielding unified conditioning for a Diffusion Transformer backbone. Experiments across ConsIDVid-Bench demonstrate that ConsID-Gen consistently outperforms in multiple metrics, with the best overall performance surpassing leading video generation models like Wan2.1 and HunyuanVideo, delivering superior identity fidelity and temporal coherence under challenging real-world scenarios. We will release our model and dataset at https://myangwu.github.io/ConsID-Gen.

Online monocular 3D reconstruction enables dense scene recovery from streaming video but remains fundamentally limited by the stability-adaptation dilemma: the reconstruction model must rapidly incorporate novel viewpoints while preserving previously accumulated scene structure. Existing streaming approaches rely on uniform or attention-based update mechanisms that often fail to account for abrupt viewpoint transitions, leading to trajectory drift and geometric inconsistencies over long sequences. We introduce PAS3R, a pose-adaptive streaming reconstruction framework that dynamically modulates state updates according to camera motion and scene structure. Our key insight is that frames contributing significant geometric novelty should exert stronger influence on the reconstruction state, while frames with minor viewpoint variation should prioritize preserving historical context. PAS3R operationalizes this principle through a motion-aware update mechanism that jointly leverages inter-frame pose variation and image frequency cues to estimate frame importance. To further stabilize long-horizon reconstruction, we introduce trajectory-consistent training objectives that incorporate relative pose constraints and acceleration regularization. A lightweight online stabilization module further suppresses high-frequency trajectory jitter and geometric artifacts without increasing memory consumption. Extensive experiments across multiple benchmarks demonstrate that PAS3R significantly improves trajectory accuracy, depth estimation, and point cloud reconstruction quality in long video sequences while maintaining competitive performance on shorter sequences.

This paper studies reference-free style-conditioned character generation in text-to-image diffusion models, where high-quality synthesis requires both stable character structure and consistent, fine-grained style expression across diverse prompts. Existing approaches primarily rely on text-only prompting, which is often under-specified for visual style and tends to produce noticeable style drift and geometric inconsistency, or introduce reference-based adapters that depend on external images at inference time, increasing architectural complexity and limiting deployment flexibility.We propose PokeFusion Attention, a lightweight decoder-level cross-attention mechanism that fuses textual semantics with learned style embeddings directly inside the diffusion decoder. By decoupling text and style conditioning at the attention level, our method enables effective reference-free stylized generation while keeping the pretrained diffusion backbone fully frozen.PokeFusion Attention trains only decoder cross-attention layers together with a compact style projection module, resulting in a parameter-efficient and plug-and-play control component that can be easily integrated into existing diffusion pipelines and transferred across different backbones.Experiments on a stylized character generation benchmark (Pokemon-style) demonstrate that our method consistently improves style fidelity, semantic alignment, and character shape consistency compared with representative adapter-based baselines, while maintaining low parameter overhead and inference-time simplicity.

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy (ρ= 0.89-0.97) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial ρ= 0.62-0.76). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks (ρapprox 0.10), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly 2times greater geometric change than CKA during post-training alignment (up to 5.23times in Llama) while providing earlier warning in 73\% of models and maintaining a 6times lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely attribute this phenomenon to optimization instability or vanishing gradients, yet such accounts fail to explain why collapse persists even under modern normalization and initialization schemes. In this paper, we argue that the collapse of deep Transformers is fundamentally a geometric problem. Standard residual updates implicitly assume that feature accumulation is always beneficial, but offer no mechanism to constrain update directions or to erase outdated information. As depth increases, this leads to systematic drift off the semantic manifold and monotonic feature accumulation, causing representational degeneracy. We propose a unified geometric framework that addresses these failures through two orthogonal principles. First, manifold-constrained hyper-connections restrict residual updates to valid local tangent directions, preventing uncontrolled manifold drift. Second, deep delta learning introduces data-dependent, non-monotonic updates that enable reflection and erasure of redundant features rather than their unconditional accumulation. Together, these mechanisms decouple the direction and sign of feature updates, yielding a stable geometric evolution across depth. We term the resulting architecture the Manifold-Geometric Transformer (MGT). Our analysis predicts that enforcing geometric validity while allowing dynamic erasure is essential for avoiding rank collapse in ultra-deep networks. We outline an evaluation protocol for Transformers exceeding 100 layers to test the hypothesis that geometry, rather than depth itself, is the key limiting factor in deep representation learning.

We analyze cumulative parameter trajectories of transformer training under AdamW and identify a dominant low-dimensional drift direction ("backbone") that captures 60--80% of long-horizon displacement from initialization. This direction is highly stable over rolling training windows yet reorients gradually across phases, particularly following objective reweighting. Per-batch gradients exhibit near-noise-floor alignment with the backbone, whereas optimizer-integrated updates align strongly with it, indicating that the structure emerges from accumulated optimizer dynamics rather than instantaneous gradient geometry. Replacing AdamW with SGD-family optimizers eliminates this structure, and reducing β_2 smoothly degrades backbone dominance and reheating recoverability. Reheating experiments show that transverse probe modes can be transiently re-excited without substantially altering accumulated backbone drift. These results provide a trajectory-level characterization of optimizer-induced geometric structure in transformer training and shift attention from instantaneous gradient properties to cumulative update dynamics.

Streaming 3D reconstruction aims to recover 3D information, such as camera poses and point clouds, from a video stream, which necessitates geometric accuracy, temporal consistency, and computational efficiency. Motivated by the principles of Simultaneous Localization and Mapping (SLAM), we introduce LingBot-Map, a feed-forward 3D foundation model for reconstructing scenes from streaming data, built upon a geometric context transformer (GCT) architecture. A defining aspect of LingBot-Map lies in its carefully designed attention mechanism, which integrates an anchor context, a pose-reference window, and a trajectory memory to address coordinate grounding, dense geometric cues, and long-range drift correction, respectively. This design keeps the streaming state compact while retaining rich geometric context, enabling stable efficient inference at around 20 FPS on 518 x 378 resolution inputs over long sequences exceeding 10,000 frames. Extensive evaluations across a variety of benchmarks demonstrate that our approach achieves superior performance compared to both existing streaming and iterative optimization-based approaches.

Analysis of learned representations has a blind spot: it focuses on similarity, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce geometric stability, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present Shesha, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated (ρapprox 0.01) and mechanistically distinct: similarity metrics collapse after removing the top principal components, while stability retains sensitivity to fine-grained manifold structure. This distinction yields actionable insights: for safety monitoring, stability acts as a functional geometric canary, detecting structural drift nearly 2times more sensitively than CKA while filtering out the non-functional noise that triggers false alarms in rigid distance metrics; for controllability, supervised stability predicts linear steerability (ρ= 0.89-0.96); for model selection, stability dissociates from transferability, revealing a geometric tax that transfer optimization incurs. Beyond machine learning, stability predicts CRISPR perturbation coherence and neural-behavioral coupling. By quantifying how reliably systems maintain structure, geometric stability provides a necessary complement to similarity for auditing representations across biological and computational systems.

Feedforward geometric foundation models achieve strong short-window reconstruction, yet scaling them to minutes-long videos is bottlenecked by quadratic attention complexity or limited effective memory in recurrent designs. We present LoGeR (Long-context Geometric Reconstruction), a novel architecture that scales dense 3D reconstruction to extremely long sequences without post-optimization. LoGeR processes video streams in chunks, leveraging strong bidirectional priors for high-fidelity intra-chunk reasoning. To manage the critical challenge of coherence across chunk boundaries, we propose a learning-based hybrid memory module. This dual-component system combines a parametric Test-Time Training (TTT) memory to anchor the global coordinate frame and prevent scale drift, alongside a non-parametric Sliding Window Attention (SWA) mechanism to preserve uncompressed context for high-precision adjacent alignment. Remarkably, this memory architecture enables LoGeR to be trained on sequences of 128 frames, and generalize up to thousands of frames during inference. Evaluated across standard benchmarks and a newly repurposed VBR dataset with sequences of up to 19k frames, LoGeR substantially outperforms prior state-of-the-art feedforward methods--reducing ATE on KITTI by over 74%--and achieves robust, globally consistent reconstruction over unprecedented horizons.

This paper presents WorldPlay, a streaming video diffusion model that enables real-time, interactive world modeling with long-term geometric consistency, resolving the trade-off between speed and memory that limits current methods. WorldPlay draws power from three key innovations. 1) We use a Dual Action Representation to enable robust action control in response to the user's keyboard and mouse inputs. 2) To enforce long-term consistency, our Reconstituted Context Memory dynamically rebuilds context from past frames and uses temporal reframing to keep geometrically important but long-past frames accessible, effectively alleviating memory attenuation. 3) We also propose Context Forcing, a novel distillation method designed for memory-aware model. Aligning memory context between the teacher and student preserves the student's capacity to use long-range information, enabling real-time speeds while preventing error drift. Taken together, WorldPlay generates long-horizon streaming 720p video at 24 FPS with superior consistency, comparing favorably with existing techniques and showing strong generalization across diverse scenes. Project page and online demo can be found: https://3d-models.hunyuan.tencent.com/world/ and https://3d.hunyuan.tencent.com/sceneTo3D.

The capacity to precisely edit genomes has outpaced our ability to predict the consequences. A cell can be genetically perfect and therapeutically useless: edited exactly as intended, yet unstable, drifting toward unintended fates, or selected for properties that compromise safety. This paradox reflects a deeper gap in how we evaluate biological intervention. Current frameworks excel at measuring what was done to a cell but remain blind to what the cell has become. We argue that this blindness stems from treating cells as collections of independent variables rather than as dynamical systems occupying positions on high-dimensional state manifolds. Drawing on Waddington's epigenetic landscape, we propose geometric stability as a missing axis of evaluation: the directional coherence of cellular responses to perturbation. This metric distinguishes interventions that guide cells coherently toward stable states from those that scatter them across the state manifold. Validation across diverse perturbation datasets reveals that geometric stability captures regulatory architecture invisible to conventional metrics, discriminating pleiotropic master regulators from lineage-specific factors without prior biological annotation. As precision medicine increasingly relies on cellular reprogramming, the question shifts from ``did the intervention occur?'' to ``is the resulting state stable?'' Geometric stability provides a framework for answering.

Current deepfake detection models achieve state-of-the-art performance on pristine academic datasets but suffer severe spatial attention drift under real-world compound degradations, such as blurring and severe lossy compression. To address this vulnerability, we propose a foundation-driven forensic framework that integrates an extreme compound degradation engine with a structurally constrained, multi-stream architecture. During training, our degradation pipeline systematically destroys high-frequency artifacts, optimizing the DINOv2-Giant backbone to extract invariant geometric and semantic priors. We then process images through three specialized pathways: a Global Texture stream, a Localized Facial stream, and a Hybrid Semantic Fusion stream incorporating CLIP. Through analyzing spatial attribution via Score-CAM and feature stability using Cosine Similarity, we quantitatively demonstrate that these streams extract non-redundant, complementary feature representations and stabilize attention entropy. By aggregating these predictions via a calibrated, discretized voting mechanism, our ensemble successfully suppresses background attention drift while acting as a robust geometric anchor. Our approach yields highly stable zero-shot generalization, achieving Fourth Place in the NTIRE 2026 Robust Deepfake Detection Challenge at CVPR. Code is available at https://github.com/khoalephanminh/ntire26-deepfake-challenge.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled RGB-only SLAM systems to achieve high-fidelity scene representation. However, the heavy reliance of existing systems on photometric rendering loss for camera tracking undermines their robustness, especially in unbounded outdoor environments with severe viewpoint and illumination changes. To address these challenges, we propose TVG-SLAM, a robust RGB-only 3DGS SLAM system that leverages a novel tri-view geometry paradigm to ensure consistent tracking and high-quality mapping. We introduce a dense tri-view matching module that aggregates reliable pairwise correspondences into consistent tri-view matches, forming robust geometric constraints across frames. For tracking, we propose Hybrid Geometric Constraints, which leverage tri-view matches to construct complementary geometric cues alongside photometric loss, ensuring accurate and stable pose estimation even under drastic viewpoint shifts and lighting variations. For mapping, we propose a new probabilistic initialization strategy that encodes geometric uncertainty from tri-view correspondences into newly initialized Gaussians. Additionally, we design a Dynamic Attenuation of Rendering Trust mechanism to mitigate tracking drift caused by mapping latency. Experiments on multiple public outdoor datasets show that our TVG-SLAM outperforms prior RGB-only 3DGS-based SLAM systems. Notably, in the most challenging dataset, our method improves tracking robustness, reducing the average Absolute Trajectory Error (ATE) by 69.0\% while achieving state-of-the-art rendering quality. The implementation of our method will be released as open-source.

Reliable odometry for legged robots without cameras or LiDAR remains challenging due to IMU drift and noisy joint velocity sensing. This paper presents a purely proprioceptive state estimator that uses only IMU and motor measurements to jointly estimate body pose and velocity, with a unified formulation applicable to biped, quadruped, and wheel-legged robots. The key idea is to treat each contacting leg as a kinematic anchor: joint-torque--based foot wrench estimation selects reliable contacts, and the corresponding footfall positions provide intermittent world-frame constraints that suppress long-term drift. To prevent elevation drift during extended traversal, we introduce a lightweight height clustering and time-decay correction that snaps newly recorded footfall heights to previously observed support planes. To improve foot velocity observations under encoder quantization, we apply an inverse-kinematics cubature Kalman filter that directly filters foot-end velocities from joint angles and velocities. The implementation further mitigates yaw drift through multi-contact geometric consistency and degrades gracefully to a kinematics-derived heading reference when IMU yaw constraints are unavailable or unreliable. We evaluate the method on four quadruped platforms (three Astrall robots and a Unitree Go2 EDU) using closed-loop trajectories. On Astrall point-foot robot~A, a sim200\,m horizontal loop and a sim15\,m vertical loop return with 0.1638\,m and 0.219\,m error, respectively; on wheel-legged robot~B, the corresponding errors are 0.2264\,m and 0.199\,m. On wheel-legged robot~C, a sim700\,m horizontal loop yields 7.68\,m error and a sim20\,m vertical loop yields 0.540\,m error. Unitree Go2 EDU closes a sim120\,m horizontal loop with 2.2138\,m error and a sim8\,m vertical loop with less than 0.1\,m vertical error. github.com/ShineMinxing/Ros2Go2Estimator.git

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from expensive divergence computation or rely on approximations of heat kernel. These limitations restrict their applicability to simple geometries and hinder scalability to high dimensions. In this work, we introduce the Riemannian Diffusion Mixture, a principled framework for building a generative diffusion process on manifolds. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes derived on general manifolds without requiring heat kernel estimations. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points that guides the process toward the data distribution. We further propose a scalable training objective for learning the mixture process that readily applies to general manifolds. Our method achieves superior performance on diverse manifolds with dramatically reduced number of in-training simulation steps for general manifolds.

While locate-then-edit knowledge editing efficiently updates knowledge encoded within Large Language Models (LLMs), a critical generalization failure mode emerges in the practical same-subject knowledge editing scenario: models fail to recall the updated knowledge when following user instructions, despite successfully recalling it in the original edited form. This paper identifies the geometric root of this generalization collapse as a fundamental conflict where the inner activation drifts induced by prompt variations exceed the model's geometric tolerance for generalization after editing. We attribute this instability to a dual pathology: (1) The joint optimization with orthogonal gradients collapses solutions into sharp minima with narrow stability, and (2) the standard covariance constraint paradoxically acts as a Covariance Trap that amplifies input perturbations. To resolve this, we introduce RoSE (Robust Same-subject Editing), which employs Isotropic Geometric Alignment to minimize representational deviation and Hierarchical Knowledge Integration to smooth the optimization landscape. Extensive experiments demonstrate that RoSE significantly improves instruction-following capabilities, laying the foundation for robust interactive parametric memory of LLM agents.

Creative face stylization aims to render portraits in diverse visual idioms such as cartoons, sketches, and paintings while retaining recognizable identity. However, current identity encoders, which are typically trained and calibrated on natural photographs, exhibit severe brittleness under stylization. They often mistake changes in texture or color palette for identity drift or fail to detect geometric exaggerations. This reveals the lack of a style-agnostic framework to evaluate and supervise identity consistency across varying styles and strengths. To address this gap, we introduce StyleID, a human perception-aware dataset and evaluation framework for facial identity under stylization. StyleID comprises two datasets: (i) StyleBench-H, a benchmark that captures human same-different verification judgments across diffusion- and flow-matching-based stylization at multiple style strengths, and (ii) StyleBench-S, a supervision set derived from psychometric recognition-strength curves obtained through controlled two-alternative forced-choice (2AFC) experiments. Leveraging StyleBench-S, we fine-tune existing semantic encoders to align their similarity orderings with human perception across styles and strengths. Experiments demonstrate that our calibrated models yield significantly higher correlation with human judgments and enhanced robustness for out-of-domain, artist drawn portraits. All of our datasets, code, and pretrained models are publicly available at https://kwanyun.github.io/StyleID_page/

Video diffusion models lack explicit geometric supervision during training, leading to inconsistency artifacts such as object deformation, spatial drift, and depth violations in generated videos. To address this limitation, we propose a geometry-based reward model that leverages pretrained geometric foundation models to evaluate multi-view consistency through cross-frame reprojection error. Unlike previous geometric metrics that measure inconsistency in pixel space, where pixel intensity may introduce additional noise, our approach conducts error computation in a pointwise fashion, yielding a more physically grounded and robust error metric. Furthermore, we introduce a geometry-aware sampling strategy that filters out low-texture and non-semantic regions, focusing evaluation on geometrically meaningful areas with reliable correspondences to improve robustness. We apply this reward model to align video diffusion models through two complementary pathways: post-training of a bidirectional model via SFT or Reinforcement Learning and inference-time optimization of a Causal Video Model (e.g., Streaming video generator) via test-time scaling with our reward as a path verifier. Experimental results validate the effectiveness of our design, demonstrating that our geometry-based reward provides superior robustness compared to other variants. By enabling efficient inference-time scaling, our method offers a practical solution for enhancing open-source video models without requiring extensive computational resources for retraining.

Despite recent progress in calibration-free monocular SLAM via 3D vision foundation models, scale drift remains severe on long sequences. Motion-agnostic partitioning breaks contextual coherence and causes zero-motion drift, while conventional geometric alignment is computationally expensive. To address these issues, we propose VGGT-Motion, a calibration-free SLAM system for efficient and robust global consistency over kilometer-scale trajectories. Specifically, we first propose a motion-aware submap construction mechanism that uses optical flow to guide adaptive partitioning, prune static redundancy, and encapsulate turns for stable local geometry. We then design an anchor-driven direct Sim(3) registration strategy. By exploiting context-balanced anchors, it achieves search-free, pixel-wise dense alignment and efficient loop closure without costly feature matching. Finally, a lightweight submap-level pose graph optimization enforces global consistency with linear complexity, enabling scalable long-range operation. Experiments show that VGGT-Motion markedly improves trajectory accuracy and efficiency, achieving state-of-the-art performance in zero-shot, long-range calibration-free monocular SLAM.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled real-time novel view synthesis (NVS) with impressive quality in indoor scenes. However, achieving high-fidelity rendering requires meticulously captured images covering the entire scene, limiting accessibility for general users. We aim to develop a practical 3DGS-based NVS framework using simple panorama-style motion with a handheld camera (e.g., mobile device). While convenient, this rotation-dominant motion and narrow baseline make accurate camera pose and 3D point estimation challenging, especially in textureless indoor scenes. To address these challenges, we propose LighthouseGS, a novel framework inspired by the lighthouse-like sweeping motion of panoramic views. LighthouseGS leverages rough geometric priors, such as mobile device camera poses and monocular depth estimation, and utilizes the planar structures often found in indoor environments. We present a new initialization method called plane scaffold assembly to generate consistent 3D points on these structures, followed by a stable pruning strategy to enhance geometry and optimization stability. Additionally, we introduce geometric and photometric corrections to resolve inconsistencies from motion drift and auto-exposure in mobile devices. Tested on collected real and synthetic indoor scenes, LighthouseGS delivers photorealistic rendering, surpassing state-of-the-art methods and demonstrating the potential for panoramic view synthesis and object placement.

Existing video depth estimation faces a fundamental trade-off: generative models suffer from stochastic geometric hallucinations and scale drift, while discriminative models demand massive labeled datasets to resolve semantic ambiguities. To break this impasse, we present DVD, the first framework to deterministically adapt pre-trained video diffusion models into single-pass depth regressors. Specifically, DVD features three core designs: (i) repurposing the diffusion timestep as a structural anchor to balance global stability with high-frequency details; (ii) latent manifold rectification (LMR) to mitigate regression-induced over-smoothing, enforcing differential constraints to restore sharp boundaries and coherent motion; and (iii) global affine coherence, an inherent property bounding inter-window divergence, which enables seamless long-video inference without requiring complex temporal alignment. Extensive experiments demonstrate that DVD achieves state-of-the-art zero-shot performance across benchmarks. Furthermore, DVD successfully unlocks the profound geometric priors implicit in video foundation models using 163x less task-specific data than leading baselines. Notably, we fully release our pipeline, providing the whole training suite for SOTA video depth estimation to benefit the open-source community.

Storyboarding is a core skill in visual storytelling for film, animation, and games. However, automating this process requires a system to achieve two properties that current approaches rarely satisfy simultaneously: inter-shot consistency and explicit editability. While 2D diffusion-based generators produce vivid imagery, they often suffer from identity drift along with limited geometric control; conversely, traditional 3D animation workflows are consistent and editable but require expert-heavy, labor-intensive authoring. We present StoryBlender, a grounded 3D storyboard generation framework governed by a Story-centric Reflection Scheme. At its core, we propose the StoryBlender system, which is built on a three-stage pipeline: (1) Semantic-Spatial Grounding, to construct a continuity memory graph to decouple global assets from shot-specific variables for long-horizon consistency; (2) Canonical Asset Materialization, to instantiate entities in a unified coordinate space to maintain visual identity; and (3) Spatial-Temporal Dynamics, to achieve layout design and cinematic evolution through visual metrics. By orchestrating multiple agents in a hierarchical manner within a verification loop, StoryBlender iteratively self-corrects spatial hallucinations via engine-verified feedback. The resulting native 3D scenes support direct, precise editing of cameras and visual assets while preserving unwavering multi-shot continuity. Experiments demonstrate that StoryBlender significantly improves consistency and editability over both diffusion-based and 3D-grounded baselines. Code, data, and demonstration video will be available on https://engineeringai-lab.github.io/StoryBlender/

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The exact definitions of maps, however, are often application-specific and hand-crafted for different scenarios (e.g. 3D landmarks, lines, planes, bags of visual words). We propose to represent maps as a deep neural net called MapNet, which enables learning a data-driven map representation. Unlike prior work on learning maps, MapNet exploits cheap and ubiquitous sensory inputs like visual odometry and GPS in addition to images and fuses them together for camera localization. Geometric constraints expressed by these inputs, which have traditionally been used in bundle adjustment or pose-graph optimization, are formulated as loss terms in MapNet training and also used during inference. In addition to directly improving localization accuracy, this allows us to update the MapNet (i.e., maps) in a self-supervised manner using additional unlabeled video sequences from the scene. We also propose a novel parameterization for camera rotation which is better suited for deep-learning based camera pose regression. Experimental results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar dataset show significant performance improvement over prior work. The MapNet project webpage is https://goo.gl/mRB3Au.

We present PiLoT, a unified framework that tackles UAV-based ego and target geo-localization. Conventional approaches rely on decoupled pipelines that fuse GNSS and Visual-Inertial Odometry (VIO) for ego-pose estimation, and active sensors like laser rangefinders for target localization. However, these methods are susceptible to failure in GNSS-denied environments and incur substantial hardware costs and complexity. PiLoT breaks this paradigm by directly registering live video stream against a geo-referenced 3D map. To achieve robust, accurate, and real-time performance, we introduce three key contributions: 1) a Dual-Thread Engine that decouples map rendering from core localization thread, ensuring both low latency while maintaining drift-free accuracy; 2) a large-scale synthetic dataset with precise geometric annotations (camera pose, depth maps). This dataset enables the training of a lightweight network that generalizes in a zero-shot manner from simulation to real data; and 3) a Joint Neural-Guided Stochastic-Gradient Optimizer (JNGO) that achieves robust convergence even under aggressive motion. Evaluations on a comprehensive set of public and newly collected benchmarks show that PiLoT outperforms state-of-the-art methods while running over 25 FPS on NVIDIA Jetson Orin platform. Our code and dataset is available at: https://github.com/Choyaa/PiLoT.

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of x_T as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime z=(x_t,t) that indexes the family of denoising distributions p(x_0 | x_t) across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Online 3D reconstruction requires estimating camera pose and scene geometry under strict causal and bounded-memory constraints. Existing methods often suffer from drift, jitter, or collapse on long sequences. We trace these failures to a fundamental mismatch. Streaming geometry is inherently temporally heterogeneous, with evidence ranging from short-lived correspondences to persistent global scale. However, current architectures impose uniform and pathological influence patterns. For example, sliding windows enforce hard cutoffs, while ungated recurrence and causal attention cause cache saturation and spike-like attention sinks. To resolve this, we formalize geometric propagation as an evidence influence kernel and propose HorizonStream, a long-horizon Transformer that explicitly factorizes this kernel. For the long-range temporal factor, Geometric Linear Attention learns channel-wise decay rates to enable bounded, multi-timescale propagation of geometric evidence. For the short-range spatial factor, Geometric Local Attention with Spatiotemporal RoPE performs reliable 3D matching while suppressing attention sinks. Finally, Metric Readout Tokens recover stable scale and rigid pose directly from the persistent geometric state. Extensive experiments show that HorizonStream, trained on only 48-frame clips, generalizes stably to sequences exceeding 10,000\ frames with constant memory and linear time, achieving state-of-the-art streaming 3D reconstruction performance. Project Page: https://3dagentworld.github.io/horizonstream/

Generating a street-level 3D scene from a single satellite image is a crucial yet challenging task. Current methods present a stark trade-off: geometry-colorization models achieve high geometric fidelity but are typically building-focused and lack semantic diversity. In contrast, proxy-based models use feed-forward image-to-3D frameworks to generate holistic scenes by jointly learning geometry and texture, a process that yields rich content but coarse and unstable geometry. We attribute these geometric failures to the extreme viewpoint gap and sparse, inconsistent supervision inherent in satellite-to-street data. We introduce Sat3DGen to address these fundamental challenges, which embodies a geometry-first methodology. This methodology enhances the feed-forward paradigm by integrating novel geometric constraints with a perspective-view training strategy, explicitly countering the primary sources of geometric error. This geometry-centric strategy yields a dramatic leap in both 3D accuracy and photorealism. For validation, we first constructed a new benchmark by pairing the VIGOR-OOD test set with high-resolution DSM data. On this benchmark, our method improves geometric RMSE from 6.76m to 5.20m. Crucially, this geometric leap also boosts photorealism, reducing the Fréchet Inception Distance (FID) from sim40 to 19 against the leading method, Sat2Density++, despite using no extra tailored image-quality modules. We demonstrate the versatility of our high-quality 3D assets through diverse downstream applications, including semantic-map-to-3D synthesis, multi-camera video generation, large-scale meshing, and unsupervised single-image Digital Surface Model (DSM) estimation. The code has been released on https://github.com/qianmingduowan/Sat3DGen.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

Data drift is the change in model input data that is one of the key factors leading to machine learning models performance degradation over time. Monitoring drift helps detecting these issues and preventing their harmful consequences. Meaningful drift interpretation is a fundamental step towards effective re-training of the model. In this study we propose an end-to-end framework for reliable model-agnostic change-point detection and interpretation in large task-oriented dialog systems, proven effective in multiple customer deployments. We evaluate our approach and demonstrate its benefits with a novel variant of intent classification training dataset, simulating customer requests to a dialog system. We make the data publicly available.

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge this gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize latent 3D representations. Our key insight is to guide the model's intermediate representations toward geometry-aware structure by aligning them with features from a pretrained geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing unnormalized geometric features from normalized diffusion representation. We evaluate Geometry Forcing on both camera view-conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods. Project page: https://GeometryForcing.github.io.

Large-scale video diffusion models achieve impressive visual quality, yet often fail to preserve geometric consistency. Prior approaches improve consistency either by augmenting the generator with additional modules or applying geometry-aware alignment. However, architectural modifications can compromise the generalization of internet-scale pretrained models, while existing alignment methods are limited to static scenes and rely on RGB-space rewards that require repeated VAE decoding, incurring substantial compute overhead and failing to generalize to highly dynamic real-world scenes. To preserve the pretrained capacity while improving geometric consistency, we propose VGGRPO (Visual Geometry GRPO), a latent geometry-guided framework for geometry-aware video post-training. VGGRPO introduces a Latent Geometry Model (LGM) that stitches video diffusion latents to geometry foundation models, enabling direct decoding of scene geometry from the latent space. By constructing LGM from a geometry model with 4D reconstruction capability, VGGRPO naturally extends to dynamic scenes, overcoming the static-scene limitations of prior methods. Building on this, we perform latent-space Group Relative Policy Optimization with two complementary rewards: a camera motion smoothness reward that penalizes jittery trajectories, and a geometry reprojection consistency reward that enforces cross-view geometric coherence. Experiments on both static and dynamic benchmarks show that VGGRPO improves camera stability, geometry consistency, and overall quality while eliminating costly VAE decoding, making latent-space geometry-guided reinforcement an efficient and flexible approach to world-consistent video generation.

This paper proposes AutoScape, a long-horizon driving scene generation framework. At its core is a novel RGB-D diffusion model that iteratively generates sparse, geometrically consistent keyframes, serving as reliable anchors for the scene's appearance and geometry. To maintain long-range geometric consistency, the model 1) jointly handles image and depth in a shared latent space, 2) explicitly conditions on the existing scene geometry (i.e., rendered point clouds) from previously generated keyframes, and 3) steers the sampling process with a warp-consistent guidance. Given high-quality RGB-D keyframes, a video diffusion model then interpolates between them to produce dense and coherent video frames. AutoScape generates realistic and geometrically consistent driving videos of over 20 seconds, improving the long-horizon FID and FVD scores over the prior state-of-the-art by 48.6\% and 43.0\%, respectively.

Multi-view image generation holds significant application value in computer vision, particularly in domains like 3D reconstruction, virtual reality, and augmented reality. Most existing methods, which rely on extending single images, face notable computational challenges in maintaining cross-view consistency and generating high-resolution outputs. To address these issues, we propose the Geometry-guided Multi-View Diffusion Model, which incorporates mechanisms for extracting multi-view geometric information and adjusting the intensity of geometric features to generate images that are both consistent across views and rich in detail. Specifically, we design a multi-view geometry information extraction module that leverages depth maps, normal maps, and foreground segmentation masks to construct a shared geometric structure, ensuring shape and structural consistency across different views. To enhance consistency and detail restoration during generation, we develop a decoupled geometry-enhanced attention mechanism that strengthens feature focus on key geometric details, thereby improving overall image quality and detail preservation. Furthermore, we apply an adaptive learning strategy that fine-tunes the model to better capture spatial relationships and visual coherence between the generated views, ensuring realistic results. Our model also incorporates an iterative refinement process that progressively improves the output quality through multiple stages of image generation. Finally, a dynamic geometry information intensity adjustment mechanism is proposed to adaptively regulate the influence of geometric data, optimizing overall quality while ensuring the naturalness of generated images. More details can be found on the project page: https://sobeymil.github.io/GeoMVD.com.

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}

While recent video diffusion models (VDMs) produce visually impressive results, they fundamentally struggle to maintain 3D structural consistency, often resulting in object deformation or spatial drift. We hypothesize that these failures arise because standard denoising objectives lack explicit incentives for geometric coherence. To address this, we introduce VideoGPA (Video Geometric Preference Alignment), a data-efficient self-supervised framework that leverages a geometry foundation model to automatically derive dense preference signals that guide VDMs via Direct Preference Optimization (DPO). This approach effectively steers the generative distribution toward inherent 3D consistency without requiring human annotations. VideoGPA significantly enhances temporal stability, physical plausibility, and motion coherence using minimal preference pairs, consistently outperforming state-of-the-art baselines in extensive experiments.

We introduce Animate124 (Animate-one-image-to-4D), the first work to animate a single in-the-wild image into 3D video through textual motion descriptions, an underexplored problem with significant applications. Our 4D generation leverages an advanced 4D grid dynamic Neural Radiance Field (NeRF) model, optimized in three distinct stages using multiple diffusion priors. Initially, a static model is optimized using the reference image, guided by 2D and 3D diffusion priors, which serves as the initialization for the dynamic NeRF. Subsequently, a video diffusion model is employed to learn the motion specific to the subject. However, the object in the 3D videos tends to drift away from the reference image over time. This drift is mainly due to the misalignment between the text prompt and the reference image in the video diffusion model. In the final stage, a personalized diffusion prior is therefore utilized to address the semantic drift. As the pioneering image-text-to-4D generation framework, our method demonstrates significant advancements over existing baselines, evidenced by comprehensive quantitative and qualitative assessments.

The grand vision of enabling persistent, large-scale 3D visual geometry understanding is shackled by the irreconcilable demands of scalability and long-term stability. While offline models like VGGT achieve inspiring geometry capability, their batch-based nature renders them irrelevant for live systems. Streaming architectures, though the intended solution for live operation, have proven inadequate. Existing methods either fail to support truly infinite-horizon inputs or suffer from catastrophic drift over long sequences. We shatter this long-standing dilemma with InfiniteVGGT, a causal visual geometry transformer that operationalizes the concept of a rolling memory through a bounded yet adaptive and perpetually expressive KV cache. Capitalizing on this, we devise a training-free, attention-agnostic pruning strategy that intelligently discards obsolete information, effectively ``rolling'' the memory forward with each new frame. Fully compatible with FlashAttention, InfiniteVGGT finally alleviates the compromise, enabling infinite-horizon streaming while outperforming existing streaming methods in long-term stability. The ultimate test for such a system is its performance over a truly infinite horizon, a capability that has been impossible to rigorously validate due to the lack of extremely long-term, continuous benchmarks. To address this critical gap, we introduce the Long3D benchmark, which, for the first time, enables a rigorous evaluation of continuous 3D geometry estimation on sequences about 10,000 frames. This provides the definitive evaluation platform for future research in long-term 3D geometry understanding. Code is available at: https://github.com/AutoLab-SAI-SJTU/InfiniteVGGT

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data, and on estimating local Hessian matrices of neural network loss landscapes.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

Novel view synthesis requires strong 3D geometric consistency and the ability to generate visually coherent images across diverse viewpoints. While recent camera-controlled video diffusion models show promising results, they often suffer from geometric distortions and limited camera controllability. To overcome these challenges, we introduce GeoNVS, a geometry-grounded novel-view synthesizer that enhances both geometric fidelity and camera controllability through explicit 3D geometric guidance. Our key innovation is the Gaussian Splat Feature Adapter (GS-Adapter), which lifts input-view diffusion features into 3D Gaussian representations, renders geometry-constrained novel-view features, and adaptively fuses them with diffusion features to correct geometrically inconsistent representations. Unlike prior methods that inject geometry at the input level, GS-Adapter operates in feature space, avoiding view-dependent color noise that degrades structural consistency. Its plug-and-play design enables zero-shot compatibility with diverse feed-forward geometry models without additional training, and can be adapted to other video diffusion backbones. Experiments across 9 scenes and 18 settings demonstrate state-of-the-art performance, achieving 11.3% and 14.9% improvements over SEVA and CameraCtrl, with up to 2x reduction in translation error and 7x in Chamfer Distance.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at https://ku-cvlab.github.io/GSD/.

Non-stationarity of an underlying data generating process that leads to distributional changes over time is a key characteristic of Data Streams. This phenomenon, commonly referred to as Concept Drift, has been intensively studied, and Concept Drift Detectors have been established as a class of methods for detecting such changes (drifts). For the most part, Drift Detectors compare regions (windows) of the data stream and detect drift if those windows are sufficiently dissimilar. In this work, we introduce the Window Dilemma, an observation that perceived drift is a product of windowing and not necessarily the underlying data generating process. Additionally, we highlight that drift detection is ill-posed, primarily because verification of drift events are implausible in practice. We demonstrate these contributions first by an illustrative example, followed by empirical comparisons of drift detectors against a variety of alternative adaptation strategies. Our main finding is that traditional batch learning techniques often perform better than their drift-aware counterparts further bringing into question the purpose of detectors in Stream Classification.

Reliable traffic data are essential for understanding urban mobility and developing effective traffic management strategies. This study introduces the DRone-derived Intelligence For Traffic analysis (DRIFT) dataset, a large-scale urban traffic dataset collected systematically from synchronized drone videos at approximately 250 meters altitude, covering nine interconnected intersections in Daejeon, South Korea. DRIFT provides high-resolution vehicle trajectories that include directional information, processed through video synchronization and orthomap alignment, resulting in a comprehensive dataset of 81,699 vehicle trajectories. Through our DRIFT dataset, researchers can simultaneously analyze traffic at multiple scales - from individual vehicle maneuvers like lane-changes and safety metrics such as time-to-collision to aggregate network flow dynamics across interconnected urban intersections. The DRIFT dataset is structured to enable immediate use without additional preprocessing, complemented by open-source models for object detection and trajectory extraction, as well as associated analytical tools. DRIFT is expected to significantly contribute to academic research and practical applications, such as traffic flow analysis and simulation studies. The dataset and related resources are publicly accessible at https://github.com/AIxMobility/The-DRIFT.

Long-sequence streaming 3D reconstruction remains a significant open challenge. Existing autoregressive models often fail when processing long sequences. They typically anchor poses to the first frame, which leads to attention decay, scale drift, and extrapolation errors. We introduce LongStream, a novel gauge-decoupled streaming visual geometry model for metric-scale scene reconstruction across thousands of frames. Our approach is threefold. First, we discard the first-frame anchor and predict keyframe-relative poses. This reformulates long-range extrapolation into a constant-difficulty local task. Second, we introduce orthogonal scale learning. This method fully disentangles geometry from scale estimation to suppress drift. Finally, we solve Transformer cache issues such as attention-sink reliance and long-term KV-cache contamination. We propose cache-consistent training combined with periodic cache refresh. This approach suppresses attention degradation over ultra-long sequences and reduces the gap between training and inference. Experiments show LongStream achieves state-of-the-art performance. It delivers stable, metric-scale reconstruction over kilometer-scale sequences at 18 FPS. Project Page: https://3dagentworld.github.io/longstream/

A very recent trend in generative modeling is building 3D-aware generators from 2D image collections. To induce the 3D bias, such models typically rely on volumetric rendering, which is expensive to employ at high resolutions. During the past months, there appeared more than 10 works that address this scaling issue by training a separate 2D decoder to upsample a low-resolution image (or a feature tensor) produced from a pure 3D generator. But this solution comes at a cost: not only does it break multi-view consistency (i.e. shape and texture change when the camera moves), but it also learns the geometry in a low fidelity. In this work, we show that it is possible to obtain a high-resolution 3D generator with SotA image quality by following a completely different route of simply training the model patch-wise. We revisit and improve this optimization scheme in two ways. First, we design a location- and scale-aware discriminator to work on patches of different proportions and spatial positions. Second, we modify the patch sampling strategy based on an annealed beta distribution to stabilize training and accelerate the convergence. The resulted model, named EpiGRAF, is an efficient, high-resolution, pure 3D generator, and we test it on four datasets (two introduced in this work) at 256^2 and 512^2 resolutions. It obtains state-of-the-art image quality, high-fidelity geometry and trains {approx} 2.5 times faster than the upsampler-based counterparts. Project website: https://universome.github.io/epigraf.

Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as geometric memory. Here, the model has synthesized embeddings encoding novel global relationships between all entities, including ones that do not co-occur in training. Such storage is powerful: for instance, we show how it transforms a hard reasoning task involving an ell-fold composition into an easy-to-learn 1-step navigation task. From this phenomenon, we extract fundamental aspects of neural embedding geometries that are hard to explain. We argue that the rise of such a geometry, as against a lookup of local associations, cannot be straightforwardly attributed to typical supervisory, architectural, or optimizational pressures. Counterintuitively, a geometry is learned even when it is more complex than the brute-force lookup. Then, by analyzing a connection to Node2Vec, we demonstrate how the geometry stems from a spectral bias that -- in contrast to prevailing theories -- indeed arises naturally despite the lack of various pressures. This analysis also points out to practitioners a visible headroom to make Transformer memory more strongly geometric. We hope the geometric view of parametric memory encourages revisiting the default intuitions that guide researchers in areas like knowledge acquisition, capacity, discovery, and unlearning.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models, and generalizes previous results on agnostic learning under drift.

Generating long-range, geometrically consistent video presents a fundamental dilemma: while consistency demands strict adherence to 3D geometry in pixel space, state-of-the-art generative models operate most effectively in a camera-conditioned latent space. This disconnect causes current methods to struggle with occluded areas and complex camera trajectories. To bridge this gap, we propose WorldWarp, a framework that couples a 3D structural anchor with a 2D generative refiner. To establish geometric grounding, WorldWarp maintains an online 3D geometric cache built via Gaussian Splatting (3DGS). By explicitly warping historical content into novel views, this cache acts as a structural scaffold, ensuring each new frame respects prior geometry. However, static warping inevitably leaves holes and artifacts due to occlusions. We address this using a Spatio-Temporal Diffusion (ST-Diff) model designed for a "fill-and-revise" objective. Our key innovation is a spatio-temporal varying noise schedule: blank regions receive full noise to trigger generation, while warped regions receive partial noise to enable refinement. By dynamically updating the 3D cache at every step, WorldWarp maintains consistency across video chunks. Consequently, it achieves state-of-the-art fidelity by ensuring that 3D logic guides structure while diffusion logic perfects texture. Project page: https://hyokong.github.io/worldwarp-page/{https://hyokong.github.io/worldwarp-page/}.

Recent advances in video generation enable a new paradigm for 3D scene creation: generating camera-controlled videos that simulate scene walkthroughs, then lifting them to 3D via feed-forward reconstruction techniques. This generative reconstruction approach combines the visual fidelity and creative capacity of video models with 3D outputs ready for real-time rendering and simulation. Scaling to large, complex environments requires 3D-consistent video generation over long camera trajectories with large viewpoint changes and location revisits, a setting where current video models degrade quickly. Existing methods for long-horizon generation are fundamentally limited by two forms of degradation: spatial forgetting and temporal drifting. As exploration proceeds, previously observed regions fall outside the model's temporal context, forcing the model to hallucinate structures when revisited. Meanwhile, autoregressive generation accumulates small synthesis errors over time, gradually distorting scene appearance and geometry. We present Lyra 2.0, a framework for generating persistent, explorable 3D worlds at scale. To address spatial forgetting, we maintain per-frame 3D geometry and use it solely for information routing -- retrieving relevant past frames and establishing dense correspondences with the target viewpoints -- while relying on the generative prior for appearance synthesis. To address temporal drifting, we train with self-augmented histories that expose the model to its own degraded outputs, teaching it to correct drift rather than propagate it. Together, these enable substantially longer and 3D-consistent video trajectories, which we leverage to fine-tune feed-forward reconstruction models that reliably recover high-quality 3D scenes.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

PGD adversarial training, the standard robustness method, can reduce Jacobian Frobenius norm yet worsen clean-input geometry (e.g., TDI 1.336 vs. ERM 1.093). We show this is not an implementation artifact but a theorem-level consequence of supervised learning. We prove that any encoder minimizing supervised loss must retain non-zero sensitivity along directions correlated with training labels, including directions that are nuisance at test time. This holds across proper scoring rules, architectures, and dataset sizes. We call this the geometric blind spot of supervised learning. This theorem unifies four empirical phenomena often treated separately: non-robust features, texture bias, corruption fragility, and the robustness-accuracy tradeoff. It also explains why suppressing sensitivity in one adversarial direction can redistribute sensitivity elsewhere. We introduce Trajectory Deviation Index (TDI), a diagnostic of geometric isotropy. Unlike CKA, intrinsic dimension, or Jacobian Frobenius norm alone, TDI captures the failure mode above. In our experiments, PGD attains low Frobenius norm but high TDI, while PMH attains the lowest TDI with one additional training term and no architectural changes. Across seven tasks, BERT/SST-2, and ImageNet ViT-B/16 (backbone family underlying CLIP/DINO/SAM), the blind spot is measurable and repairable. It appears at foundation-model scale, worsens with model scale and task-specific fine-tuning, and is substantially reduced by PMH. PMH also leads on non-Gaussian corruption types (blur/brightness/contrast) without corruption-specific training.

Object-level manipulation, relocating or reorienting objects in images or videos while preserving scene realism, is central to film post-production, AR, and creative editing. Yet existing methods struggle to jointly achieve three core goals: background preservation, geometric consistency under viewpoint shifts, and user-controllable transformations. Geometry-based approaches offer precise control but require explicit 3D reconstruction and generalize poorly; diffusion-based methods generalize better but lack fine-grained geometric control. We present Ctrl&Shift, an end-to-end diffusion framework to achieve geometry-consistent object manipulation without explicit 3D representations. Our key insight is to decompose manipulation into two stages, object removal and reference-guided inpainting under explicit camera pose control, and encode both within a unified diffusion process. To enable precise, disentangled control, we design a multi-task, multi-stage training strategy that separates background, identity, and pose signals across tasks. To improve generalization, we introduce a scalable real-world dataset construction pipeline that generates paired image and video samples with estimated relative camera poses. Extensive experiments demonstrate that Ctrl&Shift achieves state-of-the-art results in fidelity, viewpoint consistency, and controllability. To our knowledge, this is the first framework to unify fine-grained geometric control and real-world generalization for object manipulation, without relying on any explicit 3D modeling.

Dependable visual drone detection is crucial for the secure integration of drones into the airspace. However, drone detection accuracy is significantly affected by domain shifts due to environmental changes, varied points of view, and background shifts. To address these challenges, we present the DrIFT dataset, specifically developed for visual drone detection under domain shifts. DrIFT includes fourteen distinct domains, each characterized by shifts in point of view, synthetic-to-real data, season, and adverse weather. DrIFT uniquely emphasizes background shift by providing background segmentation maps to enable background-wise metrics and evaluation. Our new uncertainty estimation metric, MCDO-map, features lower postprocessing complexity, surpassing traditional methods. We use the MCDO-map in our uncertainty-aware unsupervised domain adaptation method, demonstrating superior performance to SOTA unsupervised domain adaptation techniques. The dataset is available at: https://github.com/CARG-uOttawa/DrIFT.git.

Continual post-training aims to extend large language models (LLMs) with new knowledge, skills, and behaviors, yet it remains unclear when sequential updates enable capability transfer and when they cause catastrophic forgetting. Existing methods mitigate forgetting through sequential fine-tuning, replay, regularization, or model merging, but offer limited criteria for determining when incorporating new updates is beneficial or harmful. In this work, we study LLM continual post-training through three questions: What drives forgetting? When do sequentially acquired capabilities transfer or interfere? How can compatibility be used to control update integration? We address these questions through task geometry: we represent each post-training task by its parameter update and study the covariance geometry induced by the update. Our central finding is that: forgetting can be considered as a state-relative update-integration failure, it arises when the covariance geometries induced by tasks misalign with the geometry of the evolving model state. Sequential updates transfer when they remain compatible with the model state shaped by previous updates, and interfere when state-relative geometry conflict becomes high. Motivated by this finding, we propose Geometry-Conflict Wasserstein Merging (GCWM), a data-free update-integration method that constructs a shared Wasserstein metric via Gaussian Wasserstein barycenters and uses geometry conflict to gate geometry-aware correction. Across Qwen3 0.6B--14B on domain-continual and capability-continual settings, GCWM consistently outperforms data-free baselines, improving retention and final performance without replay data. These results identify geometry conflict as both an explanatory signal for forgetting and a practical control signal for LLM continual post-training.

We tackle the task of geometric image editing, where an object within an image is repositioned, reoriented, or reshaped while preserving overall scene coherence. Previous diffusion-based editing methods often attempt to handle all relevant subtasks in a single step, proving difficult when transformations become large or structurally complex. We address this by proposing a decoupled pipeline that separates object transformation, source region inpainting, and target region refinement. Both inpainting and refinement are implemented using a training-free diffusion approach, FreeFine. In experiments on our new GeoBench benchmark, which contains both 2D and 3D editing scenarios, FreeFine outperforms state-of-the-art alternatives in image fidelity, and edit precision, especially under demanding transformations. Code and benchmark are available at: https://github.com/CIawevy/FreeFine

Recent advances in video generation have enabled the synthesis of high-quality and visually realistic clips using diffusion transformer models. However, most existing approaches operate purely in the 2D pixel space and lack explicit mechanisms for modeling 3D structures, often resulting in temporally inconsistent geometries, implausible motions, and structural artifacts. In this work, we introduce geometric regularization losses into video generation by augmenting latent diffusion models with per-frame depth prediction. We adopted depth as the geometric representation because of the great progress in depth prediction and its compatibility with image-based latent encoders. Specifically, to enforce structural consistency over time, we propose a multi-view geometric loss that aligns the predicted depth maps across frames within a shared 3D coordinate system. Our method bridges the gap between appearance generation and 3D structure modeling, leading to improved spatio-temporal coherence, shape consistency, and physical plausibility. Experiments across multiple datasets show that our approach produces significantly more stable and geometrically consistent results than existing baselines.

Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing resources for explaining diffusion either require an advanced theoretical foundation or focus on their neural network architectures rather than their rich geometric properties. We introduce Diffusion Explorer, an interactive tool to explain the geometric properties of diffusion models. Users can train 2D diffusion models in the browser and observe the temporal dynamics of their sampling process. Diffusion Explorer leverages interactive animation, which has been shown to be a powerful tool for making engaging visualizations of dynamic systems, making it well suited to explaining diffusion models which represent stochastic processes that evolve over time. Diffusion Explorer is open source and a live demo is available at alechelbling.com/Diffusion-Explorer.

In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry breaking is not well understood. Here, we develop a theoretical framework to study the "geometry of learning dynamics" in neural networks, and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. To build this understanding, we model the discrete learning dynamics of gradient descent using a continuous-time Lagrangian formulation, in which the learning rule corresponds to the kinetic energy and the loss function corresponds to the potential energy. Then, we identify "kinetic symmetry breaking" (KSB), the condition when the kinetic energy explicitly breaks the symmetry of the potential function. We generalize Noether's theorem known in physics to take into account KSB and derive the resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD). Finally, we apply NLD to neural networks with normalization layers and reveal how KSB introduces a mechanism of "implicit adaptive optimization", establishing an analogy between learning dynamics induced by normalization layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a ``bottom-up'' mechanistic route by reverse-engineering interpretable features or circuits to build explanatory models. While insightful, these methods often struggle to provide the high-level, predictive signals for anticipating failure in real-world deployment. Here, we propose using a ``top-down'' approach to studying generalization failures inspired by medical biomarkers: identifying system-level measurements that serve as robust indicators of a model's future performance. Rather than mapping out detailed internal mechanisms, we systematically design and test network markers to probe structure, function links, identify prognostic indicators, and validate predictions in real-world settings. In image classification, we find that task-relevant geometric properties of in-distribution (ID) object manifolds consistently forecast poor out-of-distribution (OOD) generalization. In particular, reductions in two geometric measures, effective manifold dimensionality and utility, predict weaker OOD performance across diverse architectures, optimizers, and datasets. We apply this finding to transfer learning with ImageNet-pretrained models. We consistently find that the same geometric patterns predict OOD transfer performance more reliably than ID accuracy. This work demonstrates that representational geometry can expose hidden vulnerabilities, offering more robust guidance for model selection and AI interpretability.

Generating high-quality 3D objects from textual descriptions remains a challenging problem due to computational cost, the scarcity of 3D data, and complex 3D representations. We introduce Geometry Image Diffusion (GIMDiffusion), a novel Text-to-3D model that utilizes geometry images to efficiently represent 3D shapes using 2D images, thereby avoiding the need for complex 3D-aware architectures. By integrating a Collaborative Control mechanism, we exploit the rich 2D priors of existing Text-to-Image models such as Stable Diffusion. This enables strong generalization even with limited 3D training data (allowing us to use only high-quality training data) as well as retaining compatibility with guidance techniques such as IPAdapter. In short, GIMDiffusion enables the generation of 3D assets at speeds comparable to current Text-to-Image models. The generated objects consist of semantically meaningful, separate parts and include internal structures, enhancing both usability and versatility.

Synthetic data is crucial for advancing autonomous driving (AD) systems, yet current state-of-the-art video generation models, despite their visual realism, suffer from subtle geometric distortions that limit their utility for downstream perception tasks. We identify and quantify this critical issue, demonstrating a significant performance gap in 3D object detection when using synthetic versus real data. To address this, we introduce Reinforcement Learning with Geometric Feedback (RLGF), RLGF uniquely refines video diffusion models by incorporating rewards from specialized latent-space AD perception models. Its core components include an efficient Latent-Space Windowing Optimization technique for targeted feedback during diffusion, and a Hierarchical Geometric Reward (HGR) system providing multi-level rewards for point-line-plane alignment, and scene occupancy coherence. To quantify these distortions, we propose GeoScores. Applied to models like DiVE on nuScenes, RLGF substantially reduces geometric errors (e.g., VP error by 21\%, Depth error by 57\%) and dramatically improves 3D object detection mAP by 12.7\%, narrowing the gap to real-data performance. RLGF offers a plug-and-play solution for generating geometrically sound and reliable synthetic videos for AD development.

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

Text-to-image generation models have achieved remarkable capabilities in synthesizing images, but often struggle to provide fine-grained control over the output. Existing guidance approaches, such as segmentation maps and depth maps, introduce spatial rigidity that restricts the inherent diversity of diffusion models. In this work, we introduce Deep Geometric Moments (DGM) as a novel form of guidance that encapsulates the subject's visual features and nuances through a learned geometric prior. DGMs focus specifically on the subject itself compared to DINO or CLIP features, which suffer from overemphasis on global image features or semantics. Unlike ResNets, which are sensitive to pixel-wise perturbations, DGMs rely on robust geometric moments. Our experiments demonstrate that DGM effectively balance control and diversity in diffusion-based image generation, allowing a flexible control mechanism for steering the diffusion process.

Recent feed-forward models have significantly advanced geometry perception for inferring dense 3D structure from sensor observations. However, its essential capabilities remain fragmented across multiple incompatible paradigms, including online perception, offline reconstruction, multi-modal integration, long-horizon scalability, and metric-scale estimation. We present UniT, a unified model built upon a novel Group Autoregressive Transformer, which reformulates these seemingly disparate capabilities within a single framework. The key idea is to treat groups of sensor observations as the basic autoregressive units and predict the corresponding point maps in an anchor-free and scale-adaptive manner. More specifically, diverse view configurations in both online and offline settings are naturally unified within a single group autoregression process. By varying the group size, online mode operates over multiple autoregressive steps with single-frame groups, whereas offline mode aggregates a multi-frame group in a single forward pass. Meanwhile, a queue-style KV caching mechanism ensures bounded autoregressive memory over long horizons. This is enabled by reducing long-range dependencies on early frames through anchor-free relational modeling, thereby allowing outdated memory to be discarded on the fly. To improve metric-scale generalization across scenes, a scale-adaptive geometry loss is further introduced within this framework. It couples relative geometric constraints with a partial absolute scale term, implicitly regularizing global scale and inducing a progressive transition from scale-invariant geometry to metric-scale solutions. Together with a dedicated modal attention module for integrating auxiliary modalities, UniT achieves state-of-the-art performance in unified geometry perception, as validated on ten benchmarks spanning seven representative tasks.

In federated learning (FL), the data distribution of each client may change over time, introducing both temporal and spatial data heterogeneity, known as concept drift. Data heterogeneity arises from three drift sources: real drift (a shift in the conditional distribution P(y|x)), virtual drift (a shift in the input distribution P(x)), and label drift (a shift in the label distribution P(y)). However, most existing FL methods addressing concept drift primarily focus on real drift. When clients experience virtual or label drift, these methods often fail to selectively retain useful historical knowledge, leading to catastrophic forgetting. A key challenge lies in distinguishing different sources of drift, as they require distinct adaptation strategies: real drift calls for discarding outdated data, while virtual or label drift benefits from retaining historical data. Without explicitly identifying the drift sources, a general adaptation strategy is suboptimal and may harm generalization. To address this challenge, we propose FedDAA, a dynamic clustered FL framework designed to adapt to multi-source concept drift while preserving valuable historical knowledge. Specifically, FedDAA integrates three modules: a cluster number determination module to find the optimal number of clusters; a real drift detection module to distinguish real drift from virtual/label drift; and a concept drift adaptation module to adapt to new data while retaining useful historical information. We provide theoretical convergence guarantees, and experiments show that FedDAA achieves 7.84% to 8.52% accuracy improvements over state-of-the-art methods on Fashion-MNIST, CIFAR-10, and CIFAR-100.

Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and flow-based models. In this paper, we propose a new paradigm called Drifting Models, which evolve the pushforward distribution during training and naturally admit one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet at 256 x 256 resolution, with an FID of 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

Recently, methods leveraging diffusion model priors to assist monocular geometric estimation (e.g., depth and normal) have gained significant attention due to their strong generalization ability. However, most existing works focus on estimating geometric properties within the camera coordinate system of individual video frames, neglecting the inherent ability of diffusion models to determine inter-frame correspondence. In this work, we demonstrate that, through appropriate design and fine-tuning, the intrinsic consistency of video generation models can be effectively harnessed for consistent geometric estimation. Specifically, we 1) select geometric attributes in the global coordinate system that share the same correspondence with video frames as the prediction targets, 2) introduce a novel and efficient conditioning method by reusing positional encodings, and 3) enhance performance through joint training on multiple geometric attributes that share the same correspondence. Our results achieve superior performance in predicting global geometric attributes in videos and can be directly applied to reconstruction tasks. Even when trained solely on static video data, our approach exhibits the potential to generalize to dynamic video scenes.

Multi-agent Large Language Model (LLM) systems have emerged as powerful architectures for complex task decomposition and collaborative problem-solving. However, their long-term behavioral stability remains largely unexamined. This study introduces the concept of agent drift, defined as the progressive degradation of agent behavior, decision quality, and inter-agent coherence over extended interaction sequences. We present a comprehensive theoretical framework for understanding drift phenomena, proposing three distinct manifestations: semantic drift (progressive deviation from original intent), coordination drift (breakdown in multi-agent consensus mechanisms), and behavioral drift (emergence of unintended strategies). We introduce the Agent Stability Index (ASI), a novel composite metric framework for quantifying drift across twelve dimensions, including response consistency, tool usage patterns, reasoning pathway stability, and inter-agent agreement rates. Through simulation-based analysis and theoretical modeling, we demonstrate how unchecked agent drift can lead to substantial reductions in task completion accuracy and increased human intervention requirements. We propose three mitigation strategies: episodic memory consolidation, drift-aware routing protocols, and adaptive behavioral anchoring. Theoretical analysis suggests these approaches can significantly reduce drift-related errors while maintaining system throughput. This work establishes a foundational methodology for monitoring, measuring, and mitigating agent drift in production agentic AI systems, with direct implications for enterprise deployment reliability and AI safety research.

Developing a unified pipeline that enables users to remove, re-texture, or replace objects in a versatile manner is crucial for text-guided 3D inpainting. However, there are still challenges in performing multiple 3D inpainting tasks within a unified framework: 1) Single reference inpainting methods lack robustness when dealing with views that are far from the reference view. 2) Appearance inconsistency arises when independently inpainting multi-view images with 2D diffusion priors; 3) Geometry inconsistency limits performance when there are significant geometric changes in the inpainting regions. To tackle these challenges, we introduce DiGA3D, a novel and versatile 3D inpainting pipeline that leverages diffusion models to propagate consistent appearance and geometry in a coarse-to-fine manner. First, DiGA3D develops a robust strategy for selecting multiple reference views to reduce errors during propagation. Next, DiGA3D designs an Attention Feature Propagation (AFP) mechanism that propagates attention features from the selected reference views to other views via diffusion models to maintain appearance consistency. Furthermore, DiGA3D introduces a Texture-Geometry Score Distillation Sampling (TG-SDS) loss to further improve the geometric consistency of inpainted 3D scenes. Extensive experiments on multiple 3D inpainting tasks demonstrate the effectiveness of our method. The project page is available at https://rorisis.github.io/DiGA3D/.

Large Language Models (LLMs) excel at single-turn tasks such as instruction following and summarization, yet real-world deployments require sustained multi-turn interactions where user goals and conversational context persist and evolve. A recurring challenge in this setting is context drift: the gradual divergence of a model's outputs from goal-consistent behavior across turns. Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics. In this work, we present a study of context drift in multi-turn interactions and propose a simple dynamical framework to interpret its behavior. We formalize drift as the turn-wise KL divergence between the token-level predictive distributions of the test model and a goal-consistent reference model, and propose a recurrence model that interprets its evolution as a bounded stochastic process with restoring forces and controllable interventions. We instantiate this framework in both synthetic long-horizon rewriting tasks and realistic user-agent simulations such as in tau-Bench, measuring drift for several open-weight LLMs that are used as user simulators. Our experiments consistently reveal stable, noise-limited equilibria rather than runaway degradation, and demonstrate that simple reminder interventions reliably reduce divergence in line with theoretical predictions. Together, these results suggest that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay, providing a foundation for studying and mitigating context drift in extended interactions.

In statistical modelling the biggest threat is concept drift which makes the model gradually showing deteriorating performance over time. There are state of the art methodologies to detect the impact of concept drift, however general strategy considered to overcome the issue in performance is to rebuild or re-calibrate the model periodically as the variable patterns for the model changes significantly due to market change or consumer behavior change etc. Quantitative research is the most widely spread application of data science in Marketing or financial domain where applicability of state of the art reinforcement learning for auto-learning is less explored paradigm. Reinforcement learning is heavily dependent on having a simulated environment which is majorly available for gaming or online systems, to learn from the live feedback. However, there are some research happened on the area of online advertisement, pricing etc where due to the nature of the online learning environment scope of reinforcement learning is explored. Our proposed solution is a reinforcement learning based, true self-learning algorithm which can adapt to the data change or concept drift and auto learn and self-calibrate for the new patterns of the data solving the problem of concept drift. Keywords - Reinforcement learning, Genetic Algorithm, Q-learning, Classification modelling, CMA-ES, NES, Multi objective optimization, Concept drift, Population stability index, Incremental learning, F1-measure, Predictive Modelling, Self-learning, MCTS, AlphaGo, AlphaZero

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present Proceed, a novel proactive model adaptation framework for online time series forecasting. Proceed first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, Proceed is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that Proceed brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at https://github.com/SJTU-DMTai/OnlineTSF.

Video generators are increasingly evaluated as potential world models, which requires them to encode and understand physical laws. We investigate their representation of a fundamental law: gravity. Out-of-the-box video generators consistently generate objects falling at an effectively slower acceleration. However, these physical tests are often confounded by ambiguous metric scale. We first investigate if observed physical errors are artifacts of these ambiguities (e.g., incorrect frame rate assumptions). We find that even temporal rescaling cannot correct the high-variance gravity artifacts. To rigorously isolate the underlying physical representation from these confounds, we introduce a unit-free, two-object protocol that tests the timing ratio t_1^2/t_2^2 = h_1/h_2, a relationship independent of g, focal length, and scale. This relative test reveals violations of Galileo's equivalence principle. We then demonstrate that this physical gap can be partially mitigated with targeted specialization. A lightweight low-rank adaptor fine-tuned on only 100 single-ball clips raises g_{eff} from 1.81,m/s^2 to 6.43,m/s^2 (reaching 65% of terrestrial gravity). This specialist adaptor also generalizes zero-shot to two-ball drops and inclined planes, offering initial evidence that specific physical laws can be corrected with minimal data.

Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., N!approx!30), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies.

Recent advances in generalizable 3D Gaussian Splatting (3DGS) have enabled rapid 3D scene reconstruction within seconds, eliminating the need for per-scene optimization. However, existing methods primarily follow an offline reconstruction paradigm, lacking the capacity for continuous reconstruction, which limits their applicability to online scenarios such as robotics and VR/AR. In this paper, we introduce OnlineX, a feed-forward framework that reconstructs both 3D visual appearance and language fields in an online manner using only streaming images. A key challenge in online formulation is the cumulative drift issue, which is rooted in the fundamental conflict between two opposing roles of the memory state: an active role that constantly refreshes to capture high-frequency local geometry, and a stable role that conservatively accumulates and preserves the long-term global structure. To address this, we introduce a decoupled active-to-stable state evolution paradigm. Our framework decouples the memory state into a dedicated active state and a persistent stable state, and then cohesively fuses the information from the former into the latter to achieve both fidelity and stability. Moreover, we jointly model visual appearance and language fields and incorporate an implicit Gaussian fusion module to enhance reconstruction quality. Experiments on mainstream datasets demonstrate that our method consistently outperforms prior work in novel view synthesis and semantic understanding, showcasing robust performance across input sequences of varying lengths with real-time inference speed.

Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this to a capacity bottleneck proposing computationally expensive width scaling of diffusion transformers we demonstrate that the failure is fundamentally geometric. We identify Geometric Interference as the root cause: standard Euclidean flow matching forces probability paths through the low-density interior of the hyperspherical feature space of representation encoders, rather than following the manifold surface. To resolve this, we propose Riemannian Flow Matching with Jacobi Regularization (RJF). By constraining the generative process to the manifold geodesics and correcting for curvature-induced error propagation, RJF enables standard Diffusion Transformer architectures to converge without width scaling. Our method RJF enables the standard DiT-B architecture (131M parameters) to converge effectively, achieving an FID of 3.37 where prior methods fail to converge. Code: https://github.com/amandpkr/RJF

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.

We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a designer and build up the points and curves of the final profile step by step. We demonstrate that adding construction steps between the designer's input geometry and the final profile improves generation quality in a similar way to the introduction of a chain of thought in language models. Similar to the constraints in a parametric CAD model, the construction sequences reduce the degrees of freedom in the modeled shape to a small set of parameter values which can be adjusted by the designer, allowing parametric editing with the constructed geometry evaluated to floating point precision. In addition we show that applying reinforcement learning to the construction sequences gives further improvements over a wide range of metrics, including some which were not explicitly optimized.

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate for a given task. Here, we explore the possibility that one can uncover useful geometric inductive biases by studying how training molds the Riemannian geometry induced by unconstrained neural network feature maps. We first show that at infinite width, neural networks with random parameters induce highly symmetric metrics on input space. This symmetry is broken by feature learning: networks trained to perform classification tasks learn to magnify local areas along decision boundaries. This holds in deep networks trained on high-dimensional image classification tasks, and even in self-supervised representation learning. These results begin to elucidate how training shapes the geometry induced by unconstrained neural network feature maps, laying the groundwork for an understanding of this richly nonlinear form of feature learning.

Diffusion models for single image novel view synthesis (NVS) can generate highly realistic and plausible images, but they are limited in the geometric consistency to the given relative poses. The generated images often show significant errors with respect to the epipolar constraints that should be fulfilled, as given by the target pose. In this paper we address this issue by proposing a methodology to improve the geometric correctness of images generated by a diffusion model for single image NVS. We formulate a loss function based on image matching and epipolar constraints, and optimize the starting noise in a diffusion sampling process such that the generated image should both be a realistic image and fulfill geometric constraints derived from the given target pose. Our method does not require training data or fine-tuning of the diffusion models, and we show that we can apply it to multiple state-of-the-art models for single image NVS. The method is evaluated on the MegaScenes dataset and we show that geometric consistency is improved compared to the baseline models while retaining the quality of the generated images.

Diffusion models have attracted significant attention due to the remarkable ability to create content and generate data for tasks like image classification. However, the usage of diffusion models to generate the high-quality object detection data remains an underexplored area, where not only image-level perceptual quality but also geometric conditions such as bounding boxes and camera views are essential. Previous studies have utilized either copy-paste synthesis or layout-to-image (L2I) generation with specifically designed modules to encode the semantic layouts. In this paper, we propose the GeoDiffusion, a simple framework that can flexibly translate various geometric conditions into text prompts and empower pre-trained text-to-image (T2I) diffusion models for high-quality detection data generation. Unlike previous L2I methods, our GeoDiffusion is able to encode not only the bounding boxes but also extra geometric conditions such as camera views in self-driving scenes. Extensive experiments demonstrate GeoDiffusion outperforms previous L2I methods while maintaining 4x training time faster. To the best of our knowledge, this is the first work to adopt diffusion models for layout-to-image generation with geometric conditions and demonstrate that L2I-generated images can be beneficial for improving the performance of object detectors.

Foundation models for biology and physics optimize predictive accuracy, but their internal representations systematically fail to preserve the continuous geometry of the systems they model. We identify the root cause: the Geometric Alignment Tax, an intrinsic cost of forcing continuous manifolds through discrete categorical bottlenecks. Controlled ablations on synthetic dynamical systems demonstrate that replacing cross-entropy with a continuous head on an identical encoder reduces geometric distortion by up to 8.5x, while learned codebooks exhibit a non-monotonic double bind where finer quantization worsens geometry despite improving reconstruction. Under continuous objectives, three architectures differ by 1.3x; under discrete tokenization, they diverge by 3,000x. Evaluating 14 biological foundation models with rate-distortion theory and MINE, we identify three failure regimes: Local-Global Decoupling, Representational Compression, and Geometric Vacuity. A controlled experiment confirms that Evo 2's reverse-complement robustness on real DNA reflects conserved sequence composition, not learned symmetry. No model achieves simultaneously low distortion, high mutual information, and global coherence.

3D Gaussian Splatting (3DGS) has become a popular solution in SLAM due to its high-fidelity and real-time novel view synthesis performance. However, some previous 3DGS SLAM methods employ a differentiable rendering pipeline for tracking, lack geometric priors in outdoor scenes. Other approaches introduce separate tracking modules, but they accumulate errors with significant camera movement, leading to scale drift. To address these challenges, we propose a robust RGB-only outdoor 3DGS SLAM method: S3PO-GS. Technically, we establish a self-consistent tracking module anchored in the 3DGS pointmap, which avoids cumulative scale drift and achieves more precise and robust tracking with fewer iterations. Additionally, we design a patch-based pointmap dynamic mapping module, which introduces geometric priors while avoiding scale ambiguity. This significantly enhances tracking accuracy and the quality of scene reconstruction, making it particularly suitable for complex outdoor environments. Our experiments on the Waymo, KITTI, and DL3DV datasets demonstrate that S3PO-GS achieves state-of-the-art results in novel view synthesis and outperforms other 3DGS SLAM methods in tracking accuracy. Project page: https://3dagentworld.github.io/S3PO-GS/.

Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable: a relation expressed in textual reasoning or drawing code carries no guarantee that a constraint-satisfying configuration realizes it. We observe that existing externalization methods based on rendered pixels or one-shot scripts fail to provide exact, per-action geometric guarantees. Enforcing geometric relations by algebraic definition closes this gap: the workspace becomes a constraint-checked evolving canvas. We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine. In a Propose-Draw-Verify loop, Draw2Think externalizes hypotheses onto an executable canvas, measures exact geometric quantities, and feeds structured observations back to the model, so subsequent reasoning proceeds from checked canvas state grounded by the shared workspace. This externalization makes two properties separately auditable: model-level Construction Fidelity (whether the canvas realizes the intended configuration) and engine-level Measurement Faithfulness (exact values and relations from canvas constraints). Across construction, outcome, and rendering evaluations, Draw2Think builds canvases that pass 95.9% predicate-level and 84.0% strict problem-level construction checks on GeoGoal, improves outcome accuracy by up to 4.1%/16.4% on planar/solid benchmarks, and attains 68.2%/90.5% strict/relaxed rendering scores on GenExam-math. Project page is available at https://draw2think.github.io/

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative L_{1} error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

Geometric foundation models show promise in 3D reconstruction, yet their progress is severely constrained by the scarcity of diverse, large-scale 3D annotations. While Internet videos offer virtually unlimited raw data, utilizing them as a scaling source for geometric learning is challenging due to the absence of ground-truth geometry and the presence of observational noise. To address this, we propose SAGE, a framework for Scalable Adaptation of GEometric foundation models from raw video streams. SAGE leverages a hierarchical mining pipeline to transform videos into training trajectories and hybrid supervision: (1) Informative training trajectory selection; (2) Sparse Geometric Anchoring via SfM point clouds for global structural guidance; and (3) Dense Differentiable Consistency via 3D Gaussian rendering for multi-view constraints. To prevent catastrophic forgetting, we introduce a regularization strategy using anchor data. Extensive experiments show that SAGE significantly enhances zero-shot generalization, reducing Chamfer Distance by 20-42% on unseen benchmarks (7Scenes, TUM-RGBD, Matterport3D) compared to state-of-the-art baselines. To our knowledge, SAGE pioneers the adaptation of geometric foundation models via Internet video, establishing a scalable paradigm for general-purpose 3D learning.

Camera redirection aims to replay a dynamic scene from a single monocular video under a user-specified camera trajectory. However, large-angle redirection is inherently ill-posed: a monocular video captures only a narrow spatio-temporal view of a dynamic 3D scene, providing highly partial observations of the underlying 4D world. The key challenge is therefore to recover a complete and coherent representation from this limited input, with consistent geometry and motion. While recent diffusion-based methods achieve impressive results, they often break down under large-angle viewpoint changes far from the original trajectory, where missing visual grounding leads to severe geometric ambiguity and temporal inconsistency. To address this, we present FreeOrbit4D, an effective training-free framework that tackles this geometric ambiguity by recovering a geometry-complete 4D proxy as structural grounding for video generation. We obtain this proxy by decoupling foreground and background reconstructions: we unproject the monocular video into a static background and geometry-incomplete foreground point clouds in a unified global space, then leverage an object-centric multi-view diffusion model to synthesize multi-view images and reconstruct geometry-complete foreground point clouds in canonical object space. By aligning the canonical foreground point cloud to the global scene space via dense pixel-synchronized 3D--3D correspondences and projecting the geometry-complete 4D proxy onto target camera viewpoints, we provide geometric scaffolds that guide a conditional video diffusion model. Extensive experiments show that FreeOrbit4D produces more faithful redirected videos under challenging large-angle trajectories, and our geometry-complete 4D proxy further opens a potential avenue for practical applications such as edit propagation and 4D data generation. Project page and code will be released soon.

Model merging aims to combine multiple models into one without additional training. Naïve parameter-space averaging can be fragile under architectural symmetries, as their geometry does not take them into account. In this work we show that not only the geometry, but also the averaging procedure itself, must be symmetry-invariant to achieve symmetry-aware merges. Consequently, we propose a general solution: merging as Fréchet averaging, i.e., selecting parameters that minimize a sum of geodesic distances on an appropriate manifold. In this view, the key design choice is the overall geometry, i.e., the choice of metric, manifold, and distance approximation, that determines what it means for two models to be "close". We show that Fréchet averaging, combined with simplifying assumptions, contains Fisher merging. Building on this, we examine the particular case of low-rank adapters (LoRA), whose symmetries induce a distinct geometry: that of a quotient manifold. We outline the limitations of current LoRA merging methods, propose a practical algorithm for this setting, and show how they compare with other commonly used approaches.

Given a monocular video, the goal of video re-rendering is to generate views of the scene from a novel camera trajectory. Existing methods face two distinct challenges. Geometrically unconditioned models lack spatial awareness, leading to drift and deformation under viewpoint changes. On the other hand, geometrically-conditioned models depend on estimated depth and explicit reconstruction, making them susceptible to depth inaccuracies and calibration errors. We propose to address these challenges by using the implicit geometric knowledge embedded in the latent space of a large 4D reconstruction model to condition the video generation process. These latents capture scene structure in a continuous space without explicit reconstruction. Therefore, they provide a flexible representation that allows the pretrained diffusion prior to regularize errors more effectively. By jointly conditioning on these latents and source camera poses, we demonstrate that our model achieves state-of-the-art results on the video re-rendering task. Project webpage is https://lavr-4d-scene-rerender.github.io/

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

Interactive world models continually generate video by responding to a user's actions, enabling open-ended generation capabilities. However, existing models typically lack a 3D representation of the environment, meaning 3D consistency must be implicitly learned from data, and spatial memory is restricted to limited temporal context windows. This results in an unrealistic user experience and presents significant obstacles to down-stream tasks such as training agents. To address this, we present PERSIST, a new paradigm of world model which simulates the evolution of a latent 3D scene: environment, camera, and renderer. This allows us to synthesize new frames with persistent spatial memory and consistent geometry. Both quantitative metrics and a qualitative user study show substantial improvements in spatial memory, 3D consistency, and long-horizon stability over existing methods, enabling coherent, evolving 3D worlds. We further demonstrate novel capabilities, including synthesising diverse 3D environments from a single image, as well as enabling fine-grained, geometry-aware control over generated experiences by supporting environment editing and specification directly in 3D space. Project page: https://francelico.github.io/persist.github.io

To address the data scarcity associated with 3D assets, 2D-lifting techniques such as Score Distillation Sampling (SDS) have become a widely adopted practice in text-to-3D generation pipelines. However, the diffusion models used in these techniques are prone to viewpoint bias and thus lead to geometric inconsistencies such as the Janus problem. To counter this, we introduce MT3D, a text-to-3D generative model that leverages a high-fidelity 3D object to overcome viewpoint bias and explicitly infuse geometric understanding into the generation pipeline. Firstly, we employ depth maps derived from a high-quality 3D model as control signals to guarantee that the generated 2D images preserve the fundamental shape and structure, thereby reducing the inherent viewpoint bias. Next, we utilize deep geometric moments to ensure geometric consistency in the 3D representation explicitly. By incorporating geometric details from a 3D asset, MT3D enables the creation of diverse and geometrically consistent objects, thereby improving the quality and usability of our 3D representations.

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

Pixel-based reinforcement learning agents often fail under purely visual distribution shift even when latent dynamics and rewards are unchanged, but existing benchmarks entangle multiple sources of shift and hinder systematic analysis. We introduce KAGE-Env, a JAX-native 2D platformer that factorizes the observation process into independently controllable visual axes while keeping the underlying control problem fixed. By construction, varying a visual axis affects performance only through the induced state-conditional action distribution of a pixel policy, providing a clean abstraction for visual generalization. Building on this environment, we define KAGE-Bench, a benchmark of six known-axis suites comprising 34 train-evaluation configuration pairs that isolate individual visual shifts. Using a standard PPO-CNN baseline, we observe strong axis-dependent failures, with background and photometric shifts often collapsing success, while agent-appearance shifts are comparatively benign. Several shifts preserve forward motion while breaking task completion, showing that return alone can obscure generalization failures. Finally, the fully vectorized JAX implementation enables up to 33M environment steps per second on a single GPU, enabling fast and reproducible sweeps over visual factors. Code: https://avanturist322.github.io/KAGEBench/.

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

We study stellar core growth in simulations of merging massive (M_star>10^{11},M_odot) elliptical galaxies by a supermassive black hole (SMBH) displaced by gravitational wave induced recoil velocity. With controlled, dense sampling of the SMBH recoil velocity, we find the core radius originally formed by SMBH binary scouring can grow by a factor of 2-3 when the recoil velocity exceeds sim50 per cent of the central escape velocity, and the mass deficit grows by up to a factor of sim4. Using Bayesian inference we predict the distribution of stellar core sizes formed through this process to peak at sim1,kpc. An orbital decomposition of stellar particles within the core reveals that radial orbits dominate over tube orbits when the recoil velocity exceeds the velocity dispersion of the core, whereas tube orbits dominate for the lowest recoil kicks. A change in orbital structure is reflected in the anisotropy parameter, with a central tangential bias present only for recoil velocities less than the local stellar velocity dispersion. Emulating current integral field unit observations of the stellar line-of-sight velocity distribution, we uncover a distinct signature in the Gauss-Hermite symmetric deviation coefficient h_4 that uniquely constrains the core size due to binary scouring. This signature is insensitive to the later evolution of the stellar mass distribution due to SMBH recoil. Our results provide a novel method to estimate the SMBH recoil magnitude from observations of local elliptical galaxies, and implies these galaxies primarily experienced recoil velocities less than the stellar velocity dispersion of the core.