Daily Papers

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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/.

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/

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.

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.

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.

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.

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.

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.

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.

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.

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/.

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.

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.

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.

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.

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.

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.

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.

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.

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.

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

We introduce a diffusion-based framework that performs aligned novel view image and geometry generation via a warping-and-inpainting methodology. Unlike prior methods that require dense posed images or pose-embedded generative models limited to in-domain views, our method leverages off-the-shelf geometry predictors to predict partial geometries viewed from reference images, and formulates novel-view synthesis as an inpainting task for both image and geometry. To ensure accurate alignment between generated images and geometry, we propose cross-modal attention distillation, where attention maps from the image diffusion branch are injected into a parallel geometry diffusion branch during both training and inference. This multi-task approach achieves synergistic effects, facilitating geometrically robust image synthesis as well as well-defined geometry prediction. We further introduce proximity-based mesh conditioning to integrate depth and normal cues, interpolating between point cloud and filtering erroneously predicted geometry from influencing the generation process. Empirically, our method achieves high-fidelity extrapolative view synthesis on both image and geometry across a range of unseen scenes, delivers competitive reconstruction quality under interpolation settings, and produces geometrically aligned colored point clouds for comprehensive 3D completion. Project page is available at https://cvlab-kaist.github.io/MoAI.

Large-scale text-to-image models enable a wide range of image editing techniques, using text prompts or even spatial controls. However, applying these editing methods to multi-view images depicting a single scene leads to 3D-inconsistent results. In this work, we focus on spatial control-based geometric manipulations and introduce a method to consolidate the editing process across various views. We build on two insights: (1) maintaining consistent features throughout the generative process helps attain consistency in multi-view editing, and (2) the queries in self-attention layers significantly influence the image structure. Hence, we propose to improve the geometric consistency of the edited images by enforcing the consistency of the queries. To do so, we introduce QNeRF, a neural radiance field trained on the internal query features of the edited images. Once trained, QNeRF can render 3D-consistent queries, which are then softly injected back into the self-attention layers during generation, greatly improving multi-view consistency. We refine the process through a progressive, iterative method that better consolidates queries across the diffusion timesteps. We compare our method to a range of existing techniques and demonstrate that it can achieve better multi-view consistency and higher fidelity to the input scene. These advantages allow us to train NeRFs with fewer visual artifacts, that are better aligned with the target geometry.

Learning to predict agent motions with relationship reasoning is important for many applications. In motion prediction tasks, maintaining motion equivariance under Euclidean geometric transformations and invariance of agent interaction is a critical and fundamental principle. However, such equivariance and invariance properties are overlooked by most existing methods. To fill this gap, we propose EqMotion, an efficient equivariant motion prediction model with invariant interaction reasoning. To achieve motion equivariance, we propose an equivariant geometric feature learning module to learn a Euclidean transformable feature through dedicated designs of equivariant operations. To reason agent's interactions, we propose an invariant interaction reasoning module to achieve a more stable interaction modeling. To further promote more comprehensive motion features, we propose an invariant pattern feature learning module to learn an invariant pattern feature, which cooperates with the equivariant geometric feature to enhance network expressiveness. We conduct experiments for the proposed model on four distinct scenarios: particle dynamics, molecule dynamics, human skeleton motion prediction and pedestrian trajectory prediction. Experimental results show that our method is not only generally applicable, but also achieves state-of-the-art prediction performances on all the four tasks, improving by 24.0/30.1/8.6/9.2%. Code is available at https://github.com/MediaBrain-SJTU/EqMotion.

We present a novel task: text-to-3D sketch animation, which aims to bring freeform sketches to life in dynamic 3D space. Unlike prior works focused on photorealistic content generation, we target sparse, stylized, and view-consistent 3D vector sketches, a lightweight and interpretable medium well-suited for visual communication and prototyping. However, this task is very challenging: (i) no paired dataset exists for text and 3D (or 4D) sketches; (ii) sketches require structural abstraction that is difficult to model with conventional 3D representations like NeRFs or point clouds; and (iii) animating such sketches demands temporal coherence and multi-view consistency, which current pipelines do not address. Therefore, we propose 4-Doodle, the first training-free framework for generating dynamic 3D sketches from text. It leverages pretrained image and video diffusion models through a dual-space distillation scheme: one space captures multi-view-consistent geometry using differentiable Bézier curves, while the other encodes motion dynamics via temporally-aware priors. Unlike prior work (e.g., DreamFusion), which optimizes from a single view per step, our multi-view optimization ensures structural alignment and avoids view ambiguity, critical for sparse sketches. Furthermore, we introduce a structure-aware motion module that separates shape-preserving trajectories from deformation-aware changes, enabling expressive motion such as flipping, rotation, and articulated movement. Extensive experiments show that our method produces temporally realistic and structurally stable 3D sketch animations, outperforming existing baselines in both fidelity and controllability. We hope this work serves as a step toward more intuitive and accessible 4D content creation.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

Large diffusion models demonstrate remarkable zero-shot capabilities in novel view synthesis from a single image. However, these models often face challenges in maintaining consistency across novel and reference views. A crucial factor leading to this issue is the limited utilization of contextual information from reference views. Specifically, when there is an overlap in the viewing frustum between two views, it is essential to ensure that the corresponding regions maintain consistency in both geometry and appearance. This observation leads to a simple yet effective approach, where we propose to use epipolar geometry to locate and retrieve overlapping information from the input view. This information is then incorporated into the generation of target views, eliminating the need for training or fine-tuning, as the process requires no learnable parameters. Furthermore, to enhance the overall consistency of generated views, we extend the utilization of epipolar attention to a multi-view setting, allowing retrieval of overlapping information from the input view and other target views. Qualitative and quantitative experimental results demonstrate the effectiveness of our method in significantly improving the consistency of synthesized views without the need for any fine-tuning. Moreover, This enhancement also boosts the performance of downstream applications such as 3D reconstruction. The code is available at https://github.com/botaoye/ConsisSyn.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

We present a novel approach to accelerate stochastic gradient descent (SGD) by utilizing curvature information obtained from Hessian-vector products or finite differences of parameters and gradients, similar to the BFGS algorithm. Our approach involves two preconditioners: a matrix-free preconditioner and a low-rank approximation preconditioner. We update both preconditioners online using a criterion that is robust to stochastic gradient noise and does not require line search or damping. To preserve the corresponding symmetry or invariance, our preconditioners are constrained to certain connected Lie groups. The Lie group's equivariance property simplifies the preconditioner fitting process, while its invariance property eliminates the need for damping, which is commonly required in second-order optimizers. As a result, the learning rate for parameter updating and the step size for preconditioner fitting are naturally normalized, and their default values work well in most scenarios. Our proposed approach offers a promising direction for improving the convergence of SGD with low computational overhead. We demonstrate that Preconditioned SGD (PSGD) outperforms SoTA on Vision, NLP, and RL tasks across multiple modern deep-learning architectures. We have provided code for reproducing toy and large scale experiments in this paper.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

Diffusion models generating images conditionally on text, such as Dall-E 2 and Stable Diffusion, have recently made a splash far beyond the computer vision community. Here, we tackle the related problem of generating point clouds, both unconditionally, and conditionally with images. For the latter, we introduce a novel geometrically-motivated conditioning scheme based on projecting sparse image features into the point cloud and attaching them to each individual point, at every step in the denoising process. This approach improves geometric consistency and yields greater fidelity than current methods relying on unstructured, global latent codes. Additionally, we show how to apply recent continuous-time diffusion schemes. Our method performs on par or above the state of art on conditional and unconditional experiments on synthetic data, while being faster, lighter, and delivering tractable likelihoods. We show it can also scale to diverse indoors scenes.

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

The increasing demand for augmented and virtual reality applications has highlighted the importance of crafting immersive 3D scenes from a simple single-view image. However, due to the partial priors provided by single-view input, existing methods are often limited to reconstruct low-consistency 3D scenes with narrow fields of view from single-view input. These limitations make them less capable of generalizing to reconstruct immersive scenes. To address this problem, we propose ExScene, a two-stage pipeline to reconstruct an immersive 3D scene from any given single-view image. ExScene designs a novel multimodal diffusion model to generate a high-fidelity and globally consistent panoramic image. We then develop a panoramic depth estimation approach to calculate geometric information from panorama, and we combine geometric information with high-fidelity panoramic image to train an initial 3D Gaussian Splatting (3DGS) model. Following this, we introduce a GS refinement technique with 2D stable video diffusion priors. We add camera trajectory consistency and color-geometric priors into the denoising process of diffusion to improve color and spatial consistency across image sequences. These refined sequences are then used to fine-tune the initial 3DGS model, leading to better reconstruction quality. Experimental results demonstrate that our ExScene achieves consistent and immersive scene reconstruction using only single-view input, significantly surpassing state-of-the-art baselines.

Text-to-3D generation from a single-view image is a popular but challenging task in 3D vision. Although numerous methods have been proposed, existing works still suffer from the inconsistency issues, including 1) semantic inconsistency, 2) geometric inconsistency, and 3) saturation inconsistency, resulting in distorted, overfitted, and over-saturated generations. In light of the above issues, we present Consist3D, a three-stage framework Chasing for semantic-, geometric-, and saturation-Consistent Text-to-3D generation from a single image, in which the first two stages aim to learn parameterized consistency tokens, and the last stage is for optimization. Specifically, the semantic encoding stage learns a token independent of views and estimations, promoting semantic consistency and robustness. Meanwhile, the geometric encoding stage learns another token with comprehensive geometry and reconstruction constraints under novel-view estimations, reducing overfitting and encouraging geometric consistency. Finally, the optimization stage benefits from the semantic and geometric tokens, allowing a low classifier-free guidance scale and therefore preventing oversaturation. Experimental results demonstrate that Consist3D produces more consistent, faithful, and photo-realistic 3D assets compared to previous state-of-the-art methods. Furthermore, Consist3D also allows background and object editing through text prompts.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

While recent advances in generative latent spaces have driven substantial progress in single-image generation, the optimal latent space for novel view synthesis (NVS) remains largely unexplored. In particular, NVS requires geometrically consistent generation across viewpoints, but existing approaches typically operate in a view-independent VAE latent space. In this paper, we propose Geometric Latent Diffusion (GLD), a framework that repurposes the geometrically consistent feature space of geometric foundation models as the latent space for multi-view diffusion. We show that these features not only support high-fidelity RGB reconstruction but also encode strong cross-view geometric correspondences, providing a well-suited latent space for NVS. Our experiments demonstrate that GLD outperforms both VAE and RAE on 2D image quality and 3D consistency metrics, while accelerating training by more than 4.4x compared to the VAE latent space. Notably, GLD remains competitive with state-of-the-art methods that leverage large-scale text-to-image pretraining, despite training its diffusion model from scratch without such generative pretraining.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Maintaining spatial world consistency over long horizons remains a central challenge for camera-controllable video generation. Existing memory-based approaches often condition generation on globally reconstructed 3D scenes by rendering anchor videos from the reconstructed geometry in the history. However, reconstructing a global 3D scene from multiple views inevitably introduces cross-view misalignment, as pose and depth estimation errors cause the same surfaces to be reconstructed at slightly different 3D locations across views. When fused, these inconsistencies accumulate into noisy geometry that contaminates the conditioning signals and degrades generation quality. We introduce AnchorWeave, a memory-augmented video generation framework that replaces a single misaligned global memory with multiple clean local geometric memories and learns to reconcile their cross-view inconsistencies. To this end, AnchorWeave performs coverage-driven local memory retrieval aligned with the target trajectory and integrates the selected local memories through a multi-anchor weaving controller during generation. Extensive experiments demonstrate that AnchorWeave significantly improves long-term scene consistency while maintaining strong visual quality, with ablation and analysis studies further validating the effectiveness of local geometric conditioning, multi-anchor control, and coverage-driven retrieval.

Text-to-3D generation has achieved significant success by incorporating powerful 2D diffusion models, but insufficient 3D prior knowledge also leads to the inconsistency of 3D geometry. Recently, since large-scale multi-view datasets have been released, fine-tuning the diffusion model on the multi-view datasets becomes a mainstream to solve the 3D inconsistency problem. However, it has confronted with fundamental difficulties regarding the limited quality and diversity of 3D data, compared with 2D data. To sidestep these trade-offs, we explore a retrieval-augmented approach tailored for score distillation, dubbed RetDream. We postulate that both expressiveness of 2D diffusion models and geometric consistency of 3D assets can be fully leveraged by employing the semantically relevant assets directly within the optimization process. To this end, we introduce novel framework for retrieval-based quality enhancement in text-to-3D generation. We leverage the retrieved asset to incorporate its geometric prior in the variational objective and adapt the diffusion model's 2D prior toward view consistency, achieving drastic improvements in both geometry and fidelity of generated scenes. We conduct extensive experiments to demonstrate that RetDream exhibits superior quality with increased geometric consistency. Project page is available at https://ku-cvlab.github.io/RetDream/.

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common visualisations of loss landscapes. By taking this geometric perspective literally and using the induced metric, we develop a new optimiser and compare it to existing methods, namely: SGD, Adam, AdamW, and Muon, across a range of tasks and architectures. Empirically, we conclude that this new class of optimisers is highly effective in low dimensional examples, and provides slight improvement over state-of-the-art methods for training neural networks. These new optimisers have theoretically desirable properties. In particular, the effective learning rate is automatically decreased in regions of high curvature acting as a smoothed out form of gradient clipping. Similarly, one variant of these optimisers can also be viewed as inducing an effective scheduled learning rate and decoupled weight decay is the natural choice from our geometric perspective. The basic method can be used to modify any existing preconditioning method. The new optimiser has a computational complexity comparable to that of Adam.

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging the inherent graph structure of EEG channels to capture the spatial relationships in brain activity. By exploiting task-specific symmetries, we define different pretraining strategies that not only improve model performance across all participant groups but also validate the robustness of the geometric representations. Explainability analysis based on the graph structures reveals consistent group-specific neural signatures that persist across pretraining conditions, suggesting stable geometric structures in the neural representations associated with motor learning and feedback processing. These geometric patterns exhibit partial invariance to certain task space transformations, indicating symmetries that enable generalisation across conditions while maintaining specificity to individual learning strategies. This work demonstrates how GNNs can uncover the effects of previous outcomes on motor planning, in a complex real-world task, providing insights into the geometric principles governing neural representations. Our experimental design bridges the gap between controlled experiments and ecologically valid scenarios, offering new insights into the organisation of neural representations during naturalistic motor learning, which may open avenues for exploring fundamental principles governing brain activity in complex tasks.

Plane Geometry Diagram Synthesis has been a crucial task in computer graphics, with applications ranging from educational tools to AI-driven mathematical reasoning. Traditionally, we rely on manual tools (e.g., Matplotlib and GeoGebra) to generate precise diagrams, but this usually requires huge, complicated calculations. Recently, researchers start to work on model-based methods (e.g., Stable Diffusion and GPT5) to automatically generate diagrams, saving operational cost but usually suffering from limited realism and insufficient accuracy. In this paper, we propose a novel framework GeoSDF, to automatically generate diagrams efficiently and accurately with Signed Distance Field (SDF). Specifically, we first represent geometric elements (e.g., points, segments, and circles) in the SDF, then construct a series of constraint functions to represent geometric relationships. Next, we optimize those constructed constraint functions to get an optimized field of both elements and constraints. Finally, by rendering the optimized field, we can obtain the synthesized diagram. In our GeoSDF, we define a symbolic language to represent geometric elements and constraints, and our synthesized geometry diagrams can be self-verified in the SDF, ensuring both mathematical accuracy and visual plausibility. In experiments, through both qualitative and quantitative analysis, GeoSDF synthesized both normal high-school level and IMO-level geometry diagrams. We achieve 88.67\% synthesis accuracy by human evaluation in the IMO problem set. Furthermore, we obtain a very high accuracy of solving geometry problems (over 95\% while the current SOTA accuracy is around 75%) by leveraging our self-verification property. All of these demonstrate the advantage of GeoSDF, paving the way for more sophisticated, accurate, and flexible generation of geometric diagrams for a wide array of applications.

In this paper, we explore the overlooked challenge of stability and temporal consistency in interactive video generation, which synthesizes dynamic and controllable video worlds through interactive behaviors such as camera movements and text prompts. Despite remarkable progress in world modeling, current methods still suffer from severe instability and temporal degradation, often leading to spatial drift and scene collapse during long-horizon interactions. To better understand this issue, we initially investigate the underlying causes of instability and identify that the major source of error accumulation originates from the same scene, where generated frames gradually deviate from the initial clean state and propagate errors to subsequent frames. Building upon this observation, we propose a simple yet effective method, StableWorld, a Dynamic Frame Eviction Mechanism. By continuously filtering out degraded frames while retaining geometrically consistent ones, StableWorld effectively prevents cumulative drift at its source, leading to more stable and temporal consistency of interactive generation. Promising results on multiple interactive video models, \eg, Matrix-Game, Open-Oasis, and Hunyuan-GameCraft, demonstrate that StableWorld is model-agnostic and can be applied to different interactive video generation frameworks to substantially improve stability, temporal consistency, and generalization across diverse interactive scenarios.

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

Mapping systems with novel view synthesis (NVS) capabilities, most notably 3D Gaussian Splatting (3DGS), are widely used in computer vision, as well as in various applications, including augmented reality, robotics, and autonomous driving. However, many current approaches are limited to static scenes. While recent works have begun addressing short-term dynamics (motion within the camera's view), long-term dynamics (the scene evolving through changes out of view) remain less explored. To overcome this limitation, we introduce a dynamic scene adaptation mechanism to continuously update 3DGS to reflect the latest changes. Since maintaining consistency remains challenging due to stale observations disrupting the reconstruction process, we further propose a novel keyframe management mechanism that discards outdated observations while preserving as much information as possible. We thoroughly evaluate Gaussian Mapping for Evolving Scenes (GaME) on both synthetic and real-world datasets, achieving a 29.7% improvement in PSNR and a 3 times improvement in L1 depth error over the most competitive baseline.

Automatic 3D generation has recently attracted widespread attention. Recent methods have greatly accelerated the generation speed, but usually produce less-detailed objects due to limited model capacity or 3D data. Motivated by recent advancements in video diffusion models, we introduce V3D, which leverages the world simulation capacity of pre-trained video diffusion models to facilitate 3D generation. To fully unleash the potential of video diffusion to perceive the 3D world, we further introduce geometrical consistency prior and extend the video diffusion model to a multi-view consistent 3D generator. Benefiting from this, the state-of-the-art video diffusion model could be fine-tuned to generate 360degree orbit frames surrounding an object given a single image. With our tailored reconstruction pipelines, we can generate high-quality meshes or 3D Gaussians within 3 minutes. Furthermore, our method can be extended to scene-level novel view synthesis, achieving precise control over the camera path with sparse input views. Extensive experiments demonstrate the superior performance of the proposed approach, especially in terms of generation quality and multi-view consistency. Our code is available at https://github.com/heheyas/V3D

While recent foundational video generators produce visually rich output, they still struggle with appearance drift, where objects gradually degrade or change inconsistently across frames, breaking visual coherence. We hypothesize that this is because there is no explicit supervision in terms of spatial tracking at the feature level. We propose Track4Gen, a spatially aware video generator that combines video diffusion loss with point tracking across frames, providing enhanced spatial supervision on the diffusion features. Track4Gen merges the video generation and point tracking tasks into a single network by making minimal changes to existing video generation architectures. Using Stable Video Diffusion as a backbone, Track4Gen demonstrates that it is possible to unify video generation and point tracking, which are typically handled as separate tasks. Our extensive evaluations show that Track4Gen effectively reduces appearance drift, resulting in temporally stable and visually coherent video generation. Project page: hyeonho99.github.io/track4gen

We present a novel video generation framework that integrates 3-dimensional geometry and dynamic awareness. To achieve this, we augment 2D videos with 3D point trajectories and align them in pixel space. The resulting 3D-aware video dataset, PointVid, is then used to fine-tune a latent diffusion model, enabling it to track 2D objects with 3D Cartesian coordinates. Building on this, we regularize the shape and motion of objects in the video to eliminate undesired artifacts, \eg, nonphysical deformation. Consequently, we enhance the quality of generated RGB videos and alleviate common issues like object morphing, which are prevalent in current video models due to a lack of shape awareness. With our 3D augmentation and regularization, our model is capable of handling contact-rich scenarios such as task-oriented videos. These videos involve complex interactions of solids, where 3D information is essential for perceiving deformation and contact. Furthermore, our model improves the overall quality of video generation by promoting the 3D consistency of moving objects and reducing abrupt changes in shape and motion.

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new L\'evy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy Flights into random walks on graphs and, as a result, allows both to accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs. Furthermore, we propose a new preferential P-DropEdge method based on the Girvan-Newman argument. That is, in contrast to uniform removing of edges as in DropEdge, following the Girvan-Newman algorithm, we detect network periphery structures using information on edge betweenness and then remove edges according to their betweenness centrality. Our experimental results on semi-supervised node classification tasks demonstrate that the LFGCN coupled with P-DropEdge accelerates the training task, increases stability and further improves predictive accuracy of learned graph topology structure. Finally, in our case studies we bring the machinery of LFGCN and other deep networks tools to analysis of power grid networks - the area where the utility of GDL remains untapped.

Multi-view 3D geometry networks offer a powerful prior but are prohibitively slow for real-time applications. We propose a novel way to adapt them for online use, enabling real-time 6-DoF pose tracking and online reconstruction of objects and scenes from monocular RGB videos. Our method rapidly selects and manages a set of images as keyframes to map a scene or object via π^3 with full bidirectional attention. We then cache the global self-attention block's key-value (KV) pairs and use them as the sole scene representation for online tracking. This allows for up to 15times speedup during inference without the fear of drift or catastrophic forgetting. Our caching strategy is model-agnostic and can be applied to other off-the-shelf multi-view networks without retraining. We demonstrate KV-Tracker on both scene-level tracking and the more challenging task of on-the-fly object tracking and reconstruction without depth measurements or object priors. Experiments on the TUM RGB-D, 7-Scenes, Arctic and OnePose datasets show the strong performance of our system while maintaining high frame-rates up to {sim}27 FPS.

In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the value of the objective function; instead, the line search can operate on merit functions. In this report, we explore an alternative line-search method which is applicable to this case; it particulary addresses the damping of the step length in tight valleys. We propose a line-search criterion based on the divergence of the field of Newton step vectors. The visualization of the criterion for two-dimensional test functions reveals a network of ravines with flat bottom at the zero points of the criterion. The ravines are typically connected to stationary points. To traverse this ravine network in order to approach a stationary point, a zigzag strategy is devised. Numerical experiments demonstrate that the novel line-search strategy succeeds from most starting points in all test functions, but only exhibits the desired damping of the step length in some situations. At the present stage it is therefore difficult to appraise the utility of this contribution.

We present 3DScenePrompt, a framework that generates the next video chunk from arbitrary-length input while enabling precise camera control and preserving scene consistency. Unlike methods conditioned on a single image or a short clip, we employ dual spatio-temporal conditioning that reformulates context-view referencing across the input video. Our approach conditions on both temporally adjacent frames for motion continuity and spatially adjacent content for scene consistency. However, when generating beyond temporal boundaries, directly using spatially adjacent frames would incorrectly preserve dynamic elements from the past. We address this by introducing a 3D scene memory that represents exclusively the static geometry extracted from the entire input video. To construct this memory, we leverage dynamic SLAM with our newly introduced dynamic masking strategy that explicitly separates static scene geometry from moving elements. The static scene representation can then be projected to any target viewpoint, providing geometrically consistent warped views that serve as strong 3D spatial prompts while allowing dynamic regions to evolve naturally from temporal context. This enables our model to maintain long-range spatial coherence and precise camera control without sacrificing computational efficiency or motion realism. Extensive experiments demonstrate that our framework significantly outperforms existing methods in scene consistency, camera controllability, and generation quality. Project page : https://cvlab-kaist.github.io/3DScenePrompt/