3D Motion

We present GeomVLA, a Vision-Language-Action (VLA) model that unifies perception, latent scene motion prediction, and action generation within a shared robot-centric 3D coordinate frame. Our approach lifts pretrained VLM features into spatially grounded 3D scene tokens using depth and camera calibration, while retaining the semantic representations learned during VLM pretraining. We further introduce a 3D Scene Trajectory Denoiser, a task-conditioned module that learns a latent representation of how scene points are expected to move in 3D. Rather than executing the predicted trajectory as an open-loop plan, GeomVLA extracts intermediate motion tokens from the trajectory denoiser and uses them to condition a 3D flow-based action denoiser through geometry-aware attention. GeomVLA achieves state-of-the-art performance on CALVIN, competitive performance on LIBERO and RoboTwin2.0, and outperforms strong baselines in real-world manipulation settings without robot-action pretraining. Extensive ablations show that future-motion reasoning alone is insufficient: the primary gains are associated with maintaining geometric consistency among scene representation, motion prediction, and robot actions throughout the perception-to-action pipeline.

Generative video models now synthesize footage nearly indistinguishable from reality. Their promise as interactive tools hinges on fine-grained control of how objects and the camera move over time, yet each existing approach captures only part of this: camera-parameter methods steer the viewpoint but cannot move objects, 2D-trajectory methods act in the image plane and ignore depth and occlusion, and recent 3D methods add geometry but run only offline at a fixed length. In particular, none combines 3D-consistent control of both camera and objects with real-time, streaming generation. Here we show that camera motion, object trajectories, and depth can be unified into a single 3D point-track representation, from which one model performs joint camera and object control, depth editing, and motion transfer in a single forward pass. To learn this interface at scale, we mine in-the-wild video for 3D motion supervision, yielding OpenVidHD-Motion3D, and encode it with a lightweight Geometric Motion Head that plugs into a pretrained video diffusion model. Because this encoder is temporally separable, we distill the model into a causal streaming student that generates arbitrarily long video in four denoising steps at memory independent of length. This unified design surpasses prior camera-only, 2D, and offline-3D methods in motion-control precision while covering modalities they address only in isolation. 4DStreamCtrl runs at 20 FPS on a single high-end GPU for 480p video and stays temporally coherent over hundreds of frames, enabling, to our knowledge, interactive 4D-controllable streaming generation for the first time. More broadly, grounding generation in explicit 3D geometry with efficient causal inference points toward interactive world models with closed-loop spatiotemporal control, from controllable simulators to real-time visual imagination for embodied agents.

Animating objects in a static 3D Gaussian scene requires an explicit object-level dynamic state and a controllable model of object motion. Existing dynamic Gaussian methods primarily reconstruct time-varying scenes or simulate deformation, rather than provide compact object states for direct control. To address this gap, we present NewtonGS, a physics-structured framework for object-level state rollout and Gaussian scene animation. NewtonGS represents each object with a 22-dimensional state covering pose, linear and angular velocity, anisotropic scale and its rate, mass, and contact properties. Its Gaussian Neural Newtonian Dynamics (Gaussian-NND) model combines analytic translation, quaternion kinematics, gravity, damping, and scale-restoration dynamics with learned continuous and contact residuals. A discrete event map handles floor contact. Predicted poses and scales define a shared affine transformation that updates the means and covariances of all Gaussians associated with each object. We construct two procedurally generated datasets: State-32 for state-rollout evaluation and Gaussian-32 for state-to-Gaussian transformation. On both the in-distribution and velocity-range-shift splits of State-32, NewtonGS achieves lower trajectory RMSE, final displacement error, and velocity RMSE than five analytic baselines. Experiments on Gaussian-32 further demonstrate effective conversion from predicted states to animated Gaussian objects.

Real-time co-speech gesture generation must produce 3D motion clip by clip as speech arrives. Existing streaming methods are open-loop: each clip depends on past context, but the model cannot check or correct its trajectory. Small errors therefore accumulate and cause drift over long sequences. We observe that this failure is mainly caused by the lack of a forward constraint rather than poor short-clip quality. A plausible key pose at the end of each clip provides a destination anchor that limits drift. Based on this observation, we propose StreamTalk, a closed-loop framework with a periodic generate-retrieve-refine cycle. Streaming Pose-Guided Generation first predicts a coarse clip, retrieves a plausible tail pose from a speaker-specific motion database, and refines the clip using this pose before continuing to the next window. During training, Stochastic Anchor Masking randomly masks pose and translation frames, teaching the model to recover complete motion from sparse boundary conditions. A part-aware DiT separates hand, body, and translation streams to reduce interference between global displacement and local articulation. On BEAT2, StreamTalk achieves state-of-the-art FGD, reduces long-horizon drift relative to open-loop baselines, and runs in real time at 76 FPS. Project page: https://xiangyue-zhang.github.io/StreamTalk/.

Pretrained video diffusion models can act as renderers when the desired scene state is already specified by an animated mesh, a camera trajectory, and a reference image. This 4D generative rendering setting raises a representation question: what image-format condition lets a video backbone obey both camera motion and scene-internal animation? We propose DAR, a reference-guided renderer that extends Wan2.2 camera control from Plücker rays alone to a joint camera-plus-geometry interface. DAR projects a neural 4D G-buffer (tracking, world position, and normal) from the animated mesh and injects it through a widened control adapter while preserving the pretrained image-to-video prior. The central design choice is the pair of tracking and world position. Tracking identifies the persistent surface element that should carry appearance; world position gives its current scene-coordinate state; normal supplies local shape. Depth plus calibrated rays can recover 3D in principle, but depth is a camera-dependent chart in which camera and object motion are mixed. On the 68-case DAR-4D benchmark, LoRA DAR reaches PSNR 23.22, SSIM 0.895, and LPIPS 0.134, improving over off-the-shelf Wan2.2-Depth by 1.54 dB PSNR; a full fine-tune reaches PSNR 25.36 and SSIM 0.917. Matched ablations show that replacing world position by depth reduces PSNR by 1.26--1.55 dB at every checkpoint, supporting tracking+world-position correspondence as a practical 4D rendering condition.

Video re-shooting aims to regenerate videos with controllable camera motion and viewpoint. Existing methods rely on explicit 3D priors, which are limited by reconstruction quality and often perform poorly when synthesizing previously unseen regions, or on paired videos with different camera trajectories, whose scarcity hinders generalization. We revisit video re-shooting through text-driven semantic viewpoint specification, enabling control over shot scale, viewing angle, and first-/third-person perspective. To this end, we propose TARS, a 3D-free video re-shooting paradigm. Timestep-wise sensitivity analysis reveals that camera motion is primarily established during high-noise stages, where coarse spatiotemporal structures are formed. Based on this insight, we introduce self-supervised training to learn camera dynamics and fundamental visual representations without paired re-shooting data or 3D reconstruction. Through data scaling and joint textual-camera conditioning, TARS supports robust camera and viewpoint control, plausibly synthesizing regions beyond the source view under large camera motions while enabling reverse-angle re-shooting and perspective switching. Extensive experiments show that TARS provides more accurate and temporally consistent camera control than prior methods. Project Page: https://ymlinfeng.github.io/TARS.github.io/

Automatically generating cinematically expressive camera trajectories through 3D scenes from natural language descriptions is a challenging task of high practical value, with applications ranging from real-estate advertising to virtual tour creation. Existing methods either lack true 3D spatial awareness by relying on 2D image priors, or treat trajectory generation as a geometric path planning problem divorced from cinematographic semantics. We present CinemaTraj, a framework that reframes camera trajectory planning as a language-grounded spatial reasoning problem. Given a set of RGB-D images and a user prompt, CinemaTraj equips an LLM agent with a structured 3D scene graph: the agent decomposes the prompt into a sequence of atomic cinematographic movements (dolly, orbit, crane, pan, tilt, zoom, arc). Each movement is instantiated via a novel parametric trajectory representation that is both cinematographically expressive and optimizable for collision avoidance. The scene graph acts as a structured spatial prior, grounding the agent's reasoning in accurate geometric and semantic knowledge of the environment. CinemaTraj further generates synchronized voiceover and subtitles aligned with camera motion, producing narrated cinematic video outputs. We evaluate CinemaTraj on real-world ScanNet++ environments, and show that it produces prompt-faithful, collision-free trajectories with high cinematographic quality, outperforming existing approaches on prompt alignment, trajectory quality, and safety metrics.

Modeling continuous object deformation is important for many computer vision and robotics tasks, such as manipulation and simulation. Existing approaches rely on learning-based methods or physics simulators to model shape deformations. However, these approaches either use discrete time steps or are too computationally intensive for real-time applications. We present ODeform, a novel extension of Neural Ordinary Differential Equations to continuous 4D dynamics of deformable objects in 3D space. Our method transforms 3D point clouds and physical conditions (like material properties) into a unified latent space. By solving the resulting ordinary differential equations over time, we model deformations as continuous flows within this learned embedding, eliminating the need for discrete time steps while maintaining computational efficiency. We evaluate our approach on unseen physical parameter configurations, showing improved motion prediction accuracy over baseline methods. Our experiments further demonstrate a successful transfer to real 3D captured objects with novel shapes, along with effective interpolation and extrapolation of the learned dynamics. Our code and data will be made publicly available.

Hand-Object Interaction (HOI) synthesis is a cornerstone for animation production and embodied AI. Despite the strong priors of video foundation models, multi-view consistent HOI synthesis remains challenging due to complex hand motions and occlusions. We present HarmoHOI, a unified diffusion framework that jointly and harmoniously generates synchronized multi-view HOI videos and globally aligned 3D point tracks. Our core insight is that robust multi-view consistency fundamentally requires globally aligned 3D geometry and motion. To this end, we propose a Mixture of Multi-view Diffusion Transformer that co-models RGB videos and 3D point tracks. By representing point tracks as pseudo-videos, we align 3D geometric signals with the 2D latent space of foundation models, thereby minimizing the domain gap and easing adaptation of priors. To further ensure geometry consistency, we introduce Global Motion Aligning Diffusion, which refines coarse point tracks into metric-scale, globally aligned 3D trajectories. HarmoHOI enables on-the-fly co-evolution of 2D appearance and 3D motion during denoising. To overcome the scarcity of multi-view HOI data, we employ a hybrid data curriculum learning strategy that successfully transfers generic priors from single-view data to synchronized multi-view generation. Experimental results show that HarmoHOI achieves state-of-the-art performance in visual quality, motion plausibility, and multi-view geometric consistency. Project page available at https://droliven.github.io/HarmoHOI_project.

Open-vocabulary 3D maps let robots answer language queries about what and where, but they assume a static world and cannot answer queries about how scene elements behave. We introduce Vision-Language-Motion Maps (VLMM), an open-vocabulary, language-queryable 3D map - queried through a rule-based intent router over open-vocabulary object nouns, not a general natural-language interface - in which each element carries a fused motion attribute: a VLM/LLM semantic movability prior combined with geometrically observed cross-frame motion, together with a per-element uncertainty. Queries reduce to attribute filters that distinguish what has been seen to move, what could move but has not, and what stays still. On a controlled simulator benchmark with exact ground truth (AI2-THOR, three scene types) we show through ablation that the schema fields are non-substitutable: a semantic-only baseline fails motion queries even with strong features, and neither motion field substitutes for the other (the prior cannot answer "what is moving," observed motion cannot answer "what could move"). On real dynamic RGB-D (TUM and Bonn, six sequences) we show the uncertainty channel - our key difference from prior fused-motion work - consistently improves moving-vs-static average precision and reduces false motion flags, and that it is robust to estimated (noisy) poses. The raw confidence is not calibrated, but post-hoc isotonic calibration reaches an expected calibration error of 0.10. VLMM is a representation contribution: the closest prior maps each lack at least one of the four properties - open-vocabulary, language-queryable, fused prior-and-observed motion, and per-element uncertainty - that our combination provides.

Modern image-and-text-to-video diffusion models can synthesize highly realistic videos by iteratively denoising an initial Gaussian noise tensor conditioned on reference image and text inputs. However, existing approaches still lack precise and unified controllability over both object motion and camera motion within a single generation process. We present UniCaMo, a unified framework that enables simultaneous control of object trajectories and camera viewpoints by directly constructing the input noise of the diffusion model. Specifically, UniCaMo builds a shared 3D-grounded motion-consistent noise space across latent video frames. Sparse 3D point tracks are used to warp the Gaussian noise of the reference frame along desired object trajectories, while a virtual spherical noise representation provides globally consistent noise values for newly revealed scene regions under camera motion. By combining local track-guided noise warping with global sphere-based noise sampling, UniCaMo maintains geometric and temporal consistency under both object movement and viewpoint changes. Because UniCaMo modifies only the input noise, it requires no auxiliary adapters, control branches, or architectural changes to the underlying video diffusion model. With lightweight LoRA fine-tuning on large pretrained video diffusion models, including Wan 2.1 (14B), UniCaMo achieves state-of-the-art results in both video quality and motion controllability on standard controllable video generation benchmarks.

We present WorldDirector, a highly controllable video world model framework designed for persistent dynamic object memory and unrestricted viewpoint exploration. Unlike existing world models that entangle physical dynamics with pixel rendering and rely on continuous visual observation to sustain motion, our framework explicitly decouples semantic motion orchestration from visual generation. By leveraging an LLM to coordinate 3D trajectories with camera movements and subsequently employing these orchestrated trajectories as control signals for video generation, our approach ensures strict physical logic and appearance stability, successfully preserving the exact visual identities of dynamic entities even when they re-enter the scene after prolonged periods out of view. Experimental results demonstrate that our method supports the synthesis of complex and extended events with unprecedented controllability and persistent dynamic object memory. Project Page: https://worlddirector.github.io/

Manipulating fast and dynamically moving targets in unstructured 3D environments remains challenging for embodied AI. Existing visual-language-action models and world models struggle with accurate 3D geometry and physically meaningful forecasting. We propose PhysMani, a framework that couples a physics-principled 3D Gaussian world model with a future-aware action policy model. The world model learns a divergence-free Gaussian velocity field via online optimization for fast and physically grounded future dynamics prediction. The policy model integrates the predicted 3D scene future dynamics through a learnable token based cross-attention module. We introduce PhysMani-Bench, a dynamic manipulation benchmark with 16 tasks, and demonstrate a superior success rate over strong baselines in both simulation and real-world robot experiments.

We present World from Motion, a method for generating freely renderable dynamic 3D Gaussian representations from monocular videos. Our approach conditions a video model on dense, pixel-aligned renderings that encode appearance, geometry, and 3D scene motion along both input and target camera trajectories to correct rendering artifacts and fill in missing regions from an initial reconstruction. To train this model, we construct a dataset of aligned multiview video pairs and dynamic 3DGS representations, with simulated artifacts characteristic of monocular reconstruction. At test time, we distill the model's generations, including newly observed regions and motions, back into a single consistent, high-quality dynamic 3DGS, improving both novel-view synthesis and the underlying 3D motion. Our method sets a new state of the art in 4D reconstruction and seamlessly generalizes to in-the-wild videos with large viewpoint changes and dynamic motions.

Video predictive models are emerging as a powerful paradigm in robotics, offering a promising path toward task generalization, long-horizon planning, and flexible decision-making. However, prevailing approaches often operate on 2D video sequences, inherently lacking the 3D geometric understanding necessary for precise spatial reasoning and physical consistency. We introduce a Structured 4D Latent Predictive Model, which predicts the evolution of a scene's 3D structure in a structured latent space conditioned on observations and textual instructions. Our representation encodes the scene holistically and can be decoded into diverse 3D formats, enabling a more complete and 3D consistent scene understanding. This structured 4D latent predictive model serves as a planner, generating future scenes that are translated into executable actions by a goal-conditioned inverse dynamics module. Experiments demonstrate that our model generates futures with strong visual quality, substantially better 3D consistency and multi-view coherence compared to state-of-the-art video-based planners. Consequently, our full planning pipeline achieves superior performance on complex manipulation tasks, exhibits robust generalization to novel visual conditions, and proves effective on real-world robotic platforms. Our website is available at https://structured-4d-model.github.io/.

Human image animation, which aims to generate a video of a reference subject following a provided action sequence, has received increasing research interest. With the development of diffusion-based/flow-based video foundation models, existing animation works have began to upgrade the guidance information from 2D skeleton/pose to 3D modeling conditions. Despite achieving reasonable results, these approaches face challenges in synthesizing trajectory-controllable human motion within natural scene under changed camera views. In this work, we present a scene-adaptive human image animation framework that controls both human motion and camera trajectories within a reconstructed 3D environment for video generation. To achieve this, we first develop a ground-adaptive 3D motion retargeting approach to enable user-friendly motion trajectory control adapting to the changes of elevations of ground and orientations automatically. Then we design a viewpoint-adaptive latent fusion mechanism to inject point-cloud geometric priors through scene-visibility masking into the generative process, providing precise guidance of viewpoint changes under camera control. Experiments on two standard human image animation benchmark datasets demonstrate remarkable improvements of our method over the state of the arts in related video generation metics. Project page: https://robinhood256100.github.io/web-disp

We present PhysiFormer, a diffusion transformer for physically-plausible 3D object motion. Unlike video world models that operate in view-dependent pixel space, PhysiFormer represents objects as 3D meshes expressed in world coordinates. Given the initial vertex positions and velocities, as well as object material type, rigid or elastic, the model samples future vertex trajectories. While related neural physics approaches build on ad-hoc latent spaces or explicitly enforce rigidity and causality, PhysiFormer shows that excellent results can be obtained without any such inductive biases, by casting vertex trajectory prediction as a single denoising diffusion process directly in world coordinates. The probabilistic formulation captures uncertainty in the learned dynamics, enabling diverse plausible futures from initial conditions, making this framework potentially useful for applications with unobserved uncertainty. The model features attention factorised over time, space, and objects for efficiency, enabling permutation-invariant multi-object reasoning without needing explicit object encoding. Trained on over 100k simulated trajectories, PhysiFormer generates rigid and elastic mechanics, and generalises to mixed-material settings, unseen real-world geometries, and larger object counts. It substantially outperforms autoregressive baselines in trajectory accuracy, rigidity preservation, and momentum-based physical consistency. Our results position coordinate-space diffusion as a promising step toward view-invariant, geometry-aware world modelling for robotics, graphics, and physical design. Visualisations, code, and models are available at https://yimingc9.github.io/physiformer.

As embodied AI and world models increasingly operate in dynamic 3D environments, visual perception must move beyond passively interpreting given observations toward actively deciding what to observe. We study this problem through camera planning in dynamic 3D story worlds, where the camera must not only generate smooth motion, but also decide what visual evidence should be acquired before it moves. We formulate this capability as Narrative-Grounded World Visual Attention, where the camera acts as an embodied observer that determines what to observe, how to compose the observation, and how to shift attention over time under narrative intent and physical 3D constraints. To realize this capability, we propose Look-Before-Move, a camera planning framework that separates observation specification from motion execution. It first builds a Semantic Observation Contract to convert directorial intent into executable visual constraints, then performs Monte Carlo Viewpoint Search to find narrative-compliant and geometrically feasible viewpoints, and finally applies Semantic Trajectory Grounding to connect selected viewpoints into continuous, collision-aware, and temporally coherent camera motion. We further construct a dynamic 3D Story World Benchmark based on StoryBlender, covering 50 stories, 457 scenes, and 1585 shots with animated characters, semantic scene configurations, and executable 3D environments. Experiments show that our framework improves subject perception, intent consistency, and trajectory quality over representative baselines, demonstrating the importance of organizing visual attention before generating camera motion.

Although text-to-motion generation has achieved strong progress in synthesizing realistic single-person motions from language, extending it to text-driven 3D human-human interaction (HHI) remains non-trivial, as HHI requires modeling the underlying \textbf{social structure} that governs phase progression, actor roles, and inter-actor coordination. In this paper, we formulate HHI generation as a social structure modeling and grounding problem: the model must first infer how an interaction unfolds and how the two actors coordinate their roles, and then realize this structure as continuous, physically plausible, and partner-aware 3D motion. To study how such structure should be modeled, we first examine the capability boundary of large language models (LLMs) for HHI generation. Our analysis shows that LLMs can \textit{think} by recovering phase decompositions and partner-aware roles, but cannot directly \textit{move}, as they fail to generate dynamic, physically plausible, and interaction-aware motion. This motivates our planner-executor paradigm, \textbf{Think with LLM, Move with Motion Skill}. The LLM planner converts implicit interaction semantics into motion-aligned social supervision by decomposing interactions into phases, assigning partner-aware actor roles, and aligning them with motion sequence. The motion executor then grounds the planned social structure into coordinated two-person motion by adapting a pretrained solo motion model with LoRA, previous-phase self-conditioning, and ego-relative partner conditioning. Together, our Solo-to-Social framework bridges social organization and motion realization, producing 3D HHI with improved phase consistency, role alignment, and partner-aware coordination.

4D dynamic scene understanding requires grounding language to a persistent worldline that binds identity, metric 3D motion, and synchronized multi-view 2D projections. Existing paradigms capture only part of this structure: large multimodal models reason over rich visual evidence but rarely preserve metric topology, while vision-language tracking remains tied to fragmented 2D or 3D outputs and local continuation. We therefore introduce \textbf{4DVLT}, a worldline-centered task for instruction-conditioned 4D dynamic scene understanding in fully observed multi-view video, and \textbf{Instruct-4D}, a benchmark with 129.4K question-answer pairs, 64.7K target entities, 851 scenes, and 9 reasoning-oriented query types. To address this setting, we present \textbf{4DTrack}, which casts instruction-conditioned tracking as graph-conditioned worldline inference through an object-centric 4D state graph, metric-guided routing, bidirectional decoding, and kinematic calibration. On Instruct-4D, 4DTrack-Qwen3.5-9B reaches 62.68 $\mathrm{TGA}_{\mathrm{Top1}}$ and surpasses the best adapted VLT baseline by 19.62 points. These results show that worldline-centered modeling improves both target grounding and recovered worldline quality. The project page is available at https://github.com/mikubaka88/4DVLT.

Motion forecasting is central to visual intelligence: agents must anticipate how objects will move in order to plan actions, reason about physical interactions, and synthesize realistic futures. We argue that 3D points in world coordinates provide a general representation that is class-agnostic, view-stable, compact, and directly useful for downstream tasks. We formalize the task of goal-conditioned 3D point motion forecasting: given a short visual history, a set of 3D query points on an object of interest, and a language description of the intended goal, the model predicts the future 3D trajectory of each point. We introduce a full stack to study this task at scale: (1) MolmoMotion-1M is a large corpus of action-described, object-grounded 3D point trajectories annotated from 1.16M unconstrained videos; (2) PointMotionBench is a human-verified benchmark spanning 111 object categories and 61 motion types; and (3) MolmoMotion is a general motion forecasting model that supports both autoregressive coordinate prediction and flow-matching-based trajectory generation. MolmoMotion accurately predicts diverse motion patterns with different language instructions, and significantly outperforms existing motion prediction baselines on PointMotionBench. Finally, we show that the learned 3D motion prior transfers well to downstream applications: it improves training efficiency and generalization for robot manipulation, and its predicted trajectories provide effective motion guidance for generative models to synthesize videos with more realistic object motion.

Safe and efficient trajectory planning in unknown, cluttered 3D environments constitutes a critical bottleneck for deploying Unmanned Aerial Vehicles (UAVs) in real-world applications. This challenge is further exacerbated by the limited field-of-view (FOV) and sensing range of onboard sensors. Many existing methods either make simplistic assumptions about unexplored space or rely on conservative heuristics such as speed limits or fixed perception patterns, reducing efficiency and generalizing poorly across different sensor types. In this work, we propose a novel planning framework that directly integrates active perception into trajectory optimization, thereby improving safety while preserving efficiency. The perception constraints are derived from the UAV's dynamic model and formulated in the sensor coordinate frame, which enables precise handling of FOV geometry. The velocity-triggered activation mechanism enables the planner to balance perception and motion efficiency. We introduce an active perception sub-trajectory segment with parametric start-time optimization, mitigating collision risks from late obstacle detection. Our formulation enables active perception during arbitrary 3D maneuvers, extending beyond prior methods designed mainly for horizontal motion. All constraints and penalties are incorporated into a differentiable optimization problem, so the planner requires only a simple front-end global path for guidance, rather than a computationally expensive perception-aware path generator. Extensive simulations and real-world experiments demonstrate robust performance across diverse unknown environments with varying sensor configurations.

Achieving fully automated, physically plausible 3D motion synthesis is a core objective in graphics and generative AI. However, configuring complex environmental force fields still relies entirely on manual expert intervention, creating a severe bottleneck for large-scale simulation data generation. Existing automated methods primarily focus on material optimization and exhibit severe modality gaps and technical flaws when applied to the vastly more complex force field optimization space: naive Large Language Models (LLMs) lack underlying simulation feedback, causing severe physical inaccuracies, while traditional Score Distillation Sampling (SDS) suffers from sluggish gradients, local optima entrapment, and a mathematical inability to dynamically switch discrete force fields. To address this, we propose PhysAgent, the first simulator-in-the-loop multi-agent framework that leverages multimodal inputs for automated, physically grounded 4D synthesis. By decoupling intrinsic materials from extrinsic dynamics, PhysAgent utilizes a Semantic Agent equipped with an externalized Force Field Skill module to master simulation rules and generate valid initializations. Subsequently, the Refine Agents, driven by Trajectory-Grounded Multi-Agent Feedback, leverage vision foundation models to extract dense point trajectories from rendered frames. By converting these explicit motion trajectories into structured textual descriptors, the agent harnesses LLM commonsense reasoning to execute zero-shot macroscopic leaps, effectively escaping local optima and dynamically switching discrete force fields. Extensive experiments demonstrate that PhysAgent rapidly generates stable, diverse physical scenes from arbitrary multimodal prompts, significantly outperforming existing baselines in both generation diversity and physical accuracy.

Video-Action Models (VAMs) leverage the broad visual dynamics captured by pre-trained video diffusion models, offering a promising path toward generalizable robot manipulation. However, RGB-only video rollouts are not directly actionable: they leave metric 3D motion, contact geometry, and fine-grained spatial constraints under-specified, making action grounding ambiguous. Meanwhile, scaling action supervision across diverse tasks and embodiments remains costly. We present PointAction, a framework that bridges video predictions to robot actions through explicit point-based 4D modeling. PointAction fine-tunes a foundation video generation model to jointly predict future RGB frames and dynamic 3D pointmaps, producing temporally consistent 3D motion of task-relevant scene geometry. These point dynamics serve as a structured, embodiment-agnostic action interface, which a diffusion-based action decoder maps to executable robot actions. By using metric 3D point dynamics as the interface between video prediction and control, PointAction reduces the ambiguity of RGB-only action grounding and supports transfer across tasks and embodiments with limited action supervision. Experiments show that PointAction achieves state-of-the-art 4D generation quality on robot scenes, outperforms existing baselines in simulation, and generalizes to two real robot arms unseen during pretraining.

Camera-controlled video generation has achieved remarkable progress in recent years. However, existing video-to-video re-rendering methods primarily rely on Supervised Fine-Tuning using synthetic datasets. At present, there is an extreme scarcity of synchronized, multi-view real-world video data. Consequently, the prevailing paradigm often exhibits limited generalization when processing out-of-distribution real-world videos, with models struggling to accurately adhere to physical scales and camera trajectories. To bridge this gap, we propose Geo-Align, the first Reinforcement Learning framework specifically designed for camera-controlled video re-rendering. Built upon a pretrained model, we optimize the model through a scale-aware perceptual reward mechanism. Specifically, we introduce a metric 3D estimator to extract precise camera trajectories from generated videos, explicitly penalizing deviations in rotation and translation. Furthermore, we meticulously designed a data pipeline strategy based on real-world conditioning videos and target camera trajectories derived from synthetic data, eliminating the reliance on paired data. Extensive experiments demonstrate that Geo-Align consistently outperforms existing supervised learning baselines in both precise camera controllability and visual fidelity, indicating the effectiveness of our method.

The adoption of vision neural networks in regulated industries requires formal robustness guarantees, especially in safety-critical domains such as healthcare, autonomous vehicles, and aerospace. However, current approaches are confined to incomplete statistical verification or robustness to $\ell_p$-norm and affine transforms, which cover only a narrow subset of perturbations to the image formation process. In particular, robustness to camera motion remains an open problem despite being key to deploy many vision applications. We present a formal verification approach that targets robustness against 3D motion perturbations of the capturing camera. We first establish a closed-form mapping from camera pose to pixel values. By analyzing the continuity properties of the resulting homographies, we show that recent work on Lipschitz optimization and piecewise continuity can be extended to derive tight linear bounds on perturbed pixel values. Our approach applies to scenes with predominantly planar structure, such as ground planes in augmented reality, road markings and traffic signs in autonomous driving, or planar workspaces in robotic manipulation. This enables the first formal verification of projective geometry transforms, without complex simulation, surrogate networks, or explicit image-formation models. We validate our implementation and show up to 89% speedup and 7% tighter bounds over prior work. We then evaluate our method on the VNN-COMP benchmark and reveal systematic weaknesses to projective perturbations. Finally, we demonstrate a real-world case study on a safety-critical runway classifier, highlighting practical vulnerabilities to camera motion, and addressing a key challenge in the certification of learned models. Data and code are publicly available at https://github.com/jeangud/homography-verification .

Generative video models are increasingly studied as implicit world models, yet evaluating whether they produce physically plausible 3D structure and motion remains challenging. Most existing video evaluation pipelines rely heavily on human judgment or learned graders, which can be subjective and weakly diagnostic for geometric failures. We introduce PDI-Bench (Perspective Distortion Index), a quantitative framework for auditing geometric coherence in generated videos. Given a generated clip, we obtain object-centric observations via segmentation and point tracking (e.g., SAM 2, MegaSaM, and CoTracker3), lift them to 3D world-space coordinates via monocular reconstruction, and compute a set of projective-geometry residuals capturing three failure dimensions: scale-depth alignment, 3D motion consistency, and 3D structural rigidity. To support systematic evaluation, we build PDI-Dataset, covering diverse scenarios designed to stress these geometric constraints. Across state-of-the-art video generators, PDI reveals consistent geometry-specific failure modes that are not captured by common perceptual metrics, and provides a diagnostic signal for progress toward physically grounded video generation and physical world model. Our code and dataset can be found at https://pdi-bench.github.io/.

We study analogical trajectory transfer, where the goal is to translate motion trajectories in one 3D environment to a semantically analogous location in another. Such a capacity would enable machines to perform analogical spatial reasoning, with applications in AR/VR co-presence, content creation, and robotics. However, even semantically similar scenes can still differ substantially in object placement, scale, and layout, so naively matching semantics leads to collisions or geometric distortions. Furthermore, finding where each trajectory point should transfer to has a large search space, as the mapping must preserve semantics and functionality without tearing the trajectory apart or causing collisions. Our key insight is to decompose the problem into spatially segregated subproblems and merge their solutions to produce semantically consistent and spatially coherent transfers. Specifically, we partition scenes into object-centric clusters and estimate cross-scene mappings via hierarchical smooth map prediction, using 3D foundation model features that encode contextual information from object and open-space arrangements. We then combinatorially assemble the per-cluster maps into an initial transfer and refine the result to remove collisions and distortions, yielding a spatially coherent trajectory. Our method does not require training, attains a fast runtime around 0.6 seconds, and outperforms baselines based on LLMs, VLMs, and scene graph matching. We further showcase applications in virtual co-presence, multi-trajectory transfer, camera transfer, and human-to-robot motion transfer, which indicates the broad applicability of our work to AR/VR and robotics.

Generating realistic human motion is a central yet unsolved challenge in video generation. While reinforcement learning (RL)-based post-training has driven recent gains in general video quality, extending it to human motion remains bottlenecked by a reward signal that cannot reliably score motion realism. Existing video rewards primarily rely on 2D perceptual signals, without explicitly modeling the 3D body state, contact, and dynamics underlying articulated human motion, and often assign high scores to videos with floating bodies or physically implausible movements. To address this, we propose PhyMotion, a structured, fine-grained motion reward that grounds recovered 3D human trajectories in a physics simulator and evaluates motion quality along multiple dimensions of physical feasibility. Concretely, we recover SMPL body meshes from generated videos, retarget them onto a humanoid in the MuJoCo physics simulator, and evaluate the resulting motion along three axes: kinematic plausibility, contact and balance consistency, and dynamic feasibility. Each component provides a continuous and interpretable signal tied to a specific aspect of motion quality, allowing the reward to capture which aspects of motion are physically correct or violated. Experiments show that PhyMotion achieves stronger correlation with human judgments than existing reward formulations. These gains carry over to RL-based post-training, where optimizing PhyMotion leads to larger and more consistent improvements than optimizing existing rewards, improving motion realism across both autoregressive and bidirectional video generators under both automatic metrics and blind human evaluation (+68 Elo gain). Ablations show that the three axes provide complementary supervision signals, while the reward preserves overall video generation quality with only modest training overhead.

Learning a physical model from video data that can comprehend physical laws and predict the future trajectories of objects is a formidable challenge in artificial intelligence. Prior approaches either leverage various Partial Differential Equations (PDEs) as soft constraints in the form of PINN losses, or integrate physics simulators into neural networks; however, they often rely on strong priors or high-quality geometry reconstruction. In this paper, we propose CausalGS, a framework that learns the causal dynamics of complex dynamic 3D scenes solely from multi-view videos, while dispensing with the reliance on explicit priors. At its core is an inverse physics inference module that decouples the complex dynamics problem from the video into the joint inference of two factors: the initial velocity field representing the scene's kinematics, and the intrinsic material properties governing its dynamics. This inferred physical information is then utilized within a differentiable physics simulator to guide the learning process in a physics-regularized manner. Extensive experiments demonstrate that CausalGS surpasses the state-of-the-art on the highly challenging task of long-term future frame extrapolation, while also exhibiting advanced performance in novel view interpolation. Crucially, our work shows that, without any human annotation, the model is able to learn the complex interactions between multiple physical properties and understand the causal relationships driving the scene's dynamic evolution, solely from visual observations.

In this paper, we introduce a challenging task: extracting a fundamental matrix from a single motion blurred image. For a camera moving in 3D during exposure, the smear paths in the blurry image contain cues and constraints on this motion. We demonstrate the feasibility of establishing correspondences between two time instances within the camera exposure window, and that these can be used to robustly infer a fundamental matrix, which summarizes the motion of the camera during the exposure time. The inferred fundamental matrix is unique up to a transpose, corresponding to an ambiguity of the direction of time. Due to this per-smear ambiguity, classic methods, such as the 8-point algorithm, are no longer usable. The proposed method modifies the estimation to work on time-direction ambiguous correspondences. To improve the robustness of the fundamental matrix estimation, we also propose to incorporate an uncertainty measurement in smear pattern prediction and use it in the sampling process of the estimator. Experiments on synthetic and real-world motion-blur datasets demonstrate that our approach is able to estimate the fundamental matrix encoding the 3D camera motion, from single frames. Practical applicability is demonstrated on the downstream task of motion segmentation.

Multi-camera systems are widely employed in sports to capture the 3D motion of athletes and equipment, yet calibrating their extrinsic parameters remains costly and labor-intensive. We introduce an efficient, tool-free method for multi-camera extrinsic calibration tailored to sports involving stick-like implements (e.g., golf clubs, bats, hockey sticks). Our approach jointly exploits two complementary cues from synchronized multi-camera videos: (i) human body keypoints with unknown metric scale and (ii) a rigid stick-like implement of known length. We formulate a three-stage optimization pipeline that refines camera extrinsics, reconstructs human and stick trajectories, and resolves global scale via the stick-length constraint. Our method achieves accurate extrinsic calibration without dedicated calibration tools. To benchmark this task, we present the first dataset for multi-camera self-calibration in stick-based sports, consisting of synthetic sequences across four sports categories with 3 to 10 cameras. Comprehensive experiments demonstrate that our method delivers SOTA performance, achieving low rotation and translation errors. Our project page: https://fandulu.github.io/sport_stick_multi_cam_calib/.

We introduce LivingWorld, an interactive framework for generating 4D worlds with environmental dynamics from a single image. While recent advances in 3D scene generation enable large-scale environment creation, most approaches focus primarily on reconstructing static geometry, leaving scene-scale environmental dynamics such as clouds, water, or smoke largely unexplored. Modeling such dynamics is challenging because motion must remain coherent across an expanding scene while supporting low-latency user feedback. LivingWorld addresses this challenge by progressively constructing a globally coherent motion field as the scene expands. To maintain global consistency during expansion, we introduce a geometry-aware alignment module that resolves directional and scale ambiguities across views. We further represent motion using a compact hash-based motion field, enabling efficient querying and stable propagation of dynamics throughout the scene. This representation also supports bidirectional motion propagation during rendering, producing long and temporally coherent 4D sequences without relying on expensive video-based refinement. On a single RTX 5090 GPU, generating each new scene expansion step requires 9 seconds, followed by 3 seconds for motion alignment and motion field updates, enabling interactive 4D world generation with globally coherent environmental dynamics. Video demonstrations are available at paper.pnu-cvsp.com/LivingWorld.

Text-guided 3D motion editing has seen success in single-person scenarios, but its extension to multi-person settings is less explored due to limited paired data and the complexity of inter-person interactions. We introduce the task of multi-person 3D motion editing, where a target motion is generated from a source and a text instruction. To support this, we propose InterEdit3D, a new dataset with manual two-person motion change annotations, and a Text-guided Multi-human Motion Editing (TMME) benchmark. We present InterEdit, a synchronized classifier-free conditional diffusion model for TMME. It introduces Semantic-Aware Plan Token Alignment with learnable tokens to capture high-level interaction cues and an Interaction-Aware Frequency Token Alignment strategy using DCT and energy pooling to model periodic motion dynamics. Experiments show that InterEdit improves text-to-motion consistency and edit fidelity, achieving state-of-the-art TMME performance. The dataset and code will be released at https://github.com/YNG916/InterEdit.

Building high-fidelity digital twins of articulated objects from visual data remains a central challenge. Existing approaches depend on multi-view captures of the object in discrete, static states, which severely constrains their real-world scalability. In this paper, we introduce Articulat3D, a novel framework that constructs such digital twins from casually captured monocular videos by jointly enforcing explicit 3D geometric and motion constraints. We first propose Motion Prior-Driven Initialization, which leverages 3D point tracks to exploit the low-dimensional structure of articulated motion. By modeling scene dynamics with a compact set of motion bases, we facilitate soft decomposition of the scene into multiple rigidly moving groups. Building on this initialization, we introduce Geometric and Motion Constraints Refinement, which enforces physically plausible articulation through learnable kinematic primitives parameterized by a joint axis, a pivot point, and per-frame motion scalars, yielding reconstructions that are both geometrically accurate and temporally coherent. Extensive experiments demonstrate that Articulat3D achieves state-of-the-art performance on synthetic benchmarks and real-world casually captured monocular videos, significantly advancing the feasibility of digital twin creation under uncontrolled real-world conditions. Our project page is available at https://maxwell-zhao.github.io/Articulat3D/.

3D Scene Graphs (3DSGs) provide hierarchical, multi-resolution abstractions that encode the geometric and semantic structure of an environment, yet their treatment of dynamics remains limited to tracking individual agents. Maps of Dynamics (MoDs) complement this by modeling aggregate motion patterns, but rely on uniform grid discretizations that lack semantic grounding and scale poorly. We present Rheos, a framework that explicitly embeds continuous directional motion models into an additional dynamics layer of a hierarchical 3DSG that enhances the navigational properties of the graph. Each dynamics node maintains a semi-wrapped Gaussian mixture model that captures multimodal directional flow as a principled probability distribution with explicit uncertainty, replacing the discrete histograms used in prior work. To enable online operation, Rheos employs reservoir sampling for bounded-memory observation buffers, parallel per-cell model updates and a principled Bayesian Information Criterion (BIC) sweep that selects the optimal number of mixture components, reducing per-update initialization cost from quadratic to linear in the number of samples. Evaluated across four spatial resolutions in a simulated pedestrian environment, Rheos consistently outperforms the discrete baseline under continuous as well as unfavorable discrete metrics. We release our implementation as open source.

Recent video diffusion models have achieved impressive capabilities as large-scale generative world models. However, these models often struggle with fine-grained physical consistency, exhibiting physically implausible dynamics over time. In this work, we present \textbf{Phys4D}, a pipeline for learning physics-consistent 4D world representations from video diffusion models. Phys4D adopts \textbf{a three-stage training paradigm} that progressively lifts appearance-driven video diffusion models into physics-consistent 4D world representations. We first bootstrap robust geometry and motion representations through large-scale pseudo-supervised pretraining, establishing a foundation for 4D scene modeling. We then perform physics-grounded supervised fine-tuning using simulation-generated data, enforcing temporally consistent 4D dynamics. Finally, we apply simulation-grounded reinforcement learning to correct residual physical violations that are difficult to capture through explicit supervision. To evaluate fine-grained physical consistency beyond appearance-based metrics, we introduce a set of \textbf{4D world consistency evaluation} that probe geometric coherence, motion stability, and long-horizon physical plausibility. Experimental results demonstrate that Phys4D substantially improves fine-grained spatiotemporal and physical consistency compared to appearance-driven baselines, while maintaining strong generative performance. Our project page is available at https://sensational-brioche-7657e7.netlify.app/

Transferring articulated motion from monocular videos to rigged 3D characters is challenging due to pose ambiguity in 2D observations and morphological differences between source and target. Existing approaches often follow a reconstruct-then-retarget paradigm, tying transfer quality to intermediate 3D reconstruction and limiting applicability to categories with parametric templates. We propose MorphGS, a framework that formulates motion retargeting as a target-driven analysis-by-synthesis problem, directly optimizing target morphology and pose through image-space supervision. A rig-coupled morphology parameterization factorizes character identity from time-varying joint rotations, while dense 2D-3D correspondences and synthesized views provide complementary structural and multi-view guidance. Experiments on synthetic benchmarks and real-world videos show consistent improvements over baselines. Project page: https://xodus777.github.io/MorphGS/

Generating interactive and dynamic 4D scenes from a single static image remains a core challenge. Most existing generate-then-reconstruct and reconstruct-then-generate methods decouple geometry from motion, causing spatiotemporal inconsistencies and poor generalization. To address these, we present MoGe4D (Motion and Geometry-Aware image-to-4D Synthesis), a geometry-conditioned framework for single-image 4D synthesis that models a scene as dense 4D point trajectories. Instead of treating geometry and dynamics as two disconnected stages, our method starts from an initial geometric prior inferred from the input image and predicts future time-varying trajectories in a diffusion process, improving spatiotemporal coherence while preserving structural stability. To support this task, we first introduce TrajScene-60K, a large-scale dataset of 60,000 video samples with dense 4D point trajectories, addressing the scarcity of high-quality training data for scene-level 4D generation. Built on this, our diffusion-based 4D Scene Trajectory Generator (4D-STraG) predicts geometry-consistent and motion-plausible trajectory fields conditioned on the input image, with a depth-guided motion normalization strategy to reduce scale ambiguity and a Motion Perception Module (MPM) to inject motion-aware priors. We further propose a 4D View Synthesis Module (4D-ViSM) to render the generated 4D representation into videos under arbitrary camera trajectories. Experiments show that MoGe4D produces high-quality 4D scenes with strong temporal coherence, favorable geometry-aware consistency, and compelling novel-view synthesis from a single image. Code: https://github.com/Zhangyr2022/MoGe4D.

This work presents an algorithm for changing from latitudinal to longitudinal formation of autonomous aircraft squadrons. The maneuvers are defined dynamically by using a predefined set of 3D basic maneuvers. This formation change is necessary when the squadron has to perform tasks which demand both formations, such as lift off, georeferencing, obstacle avoidance and landing. Simulations show that the formation change is done without collision. The time complexity analysis of the transformation algorithm reveals that its efficiency is optimal, and the proof of correctness ensures its longitudinal formation features.