Daily Papers

Generating human videos with realistic and controllable motions is a challenging task. While existing methods can generate visually compelling videos, they lack separate control over four key video elements: foreground subject, background video, human trajectory and action patterns. In this paper, we propose a decomposed human motion control and video generation framework that explicitly decouples motion from appearance, subject from background, and action from trajectory, enabling flexible mix-and-match composition of these elements. Concretely, we first build a ground-aware 3D world coordinate system and perform motion editing directly in the 3D space. Trajectory control is implemented by unprojecting edited 2D trajectories into 3D with focal-length calibration and coordinate transformation, followed by speed alignment and orientation adjustment; actions are supplied by a motion bank or generated via text-to-motion methods. Then, based on modern text-to-video diffusion transformer models, we inject the subject as tokens for full attention, concatenate the background along the channel dimension, and add motion (trajectory and action) control signals by addition. Such a design opens up the possibility for us to generate realistic videos of anyone doing anything anywhere. Extensive experiments on benchmark datasets and real-world cases demonstrate that our method achieves state-of-the-art performance on both element-wise controllability and overall video quality.

This study aims to achieve more precise and versatile object control in image-to-video (I2V) generation. Current methods typically represent the spatial movement of target objects with 2D trajectories, which often fail to capture user intention and frequently produce unnatural results. To enhance control, we present ObjCtrl-2.5D, a training-free object control approach that uses a 3D trajectory, extended from a 2D trajectory with depth information, as a control signal. By modeling object movement as camera movement, ObjCtrl-2.5D represents the 3D trajectory as a sequence of camera poses, enabling object motion control using an existing camera motion control I2V generation model (CMC-I2V) without training. To adapt the CMC-I2V model originally designed for global motion control to handle local object motion, we introduce a module to isolate the target object from the background, enabling independent local control. In addition, we devise an effective way to achieve more accurate object control by sharing low-frequency warped latent within the object's region across frames. Extensive experiments demonstrate that ObjCtrl-2.5D significantly improves object control accuracy compared to training-free methods and offers more diverse control capabilities than training-based approaches using 2D trajectories, enabling complex effects like object rotation. Code and results are available at https://wzhouxiff.github.io/projects/ObjCtrl-2.5D/.

Recovering 4D from monocular video, which jointly estimates dynamic geometry and camera poses, is an inevitably challenging problem. While recent pointmap-based 3D reconstruction methods (e.g., DUSt3R) have made great progress in reconstructing static scenes, directly applying them to dynamic scenes leads to inaccurate results. This discrepancy arises because moving objects violate multi-view geometric constraints, disrupting the reconstruction. To address this, we introduce C4D, a framework that leverages temporal Correspondences to extend existing 3D reconstruction formulation to 4D. Specifically, apart from predicting pointmaps, C4D captures two types of correspondences: short-term optical flow and long-term point tracking. We train a dynamic-aware point tracker that provides additional mobility information, facilitating the estimation of motion masks to separate moving elements from the static background, thus offering more reliable guidance for dynamic scenes. Furthermore, we introduce a set of dynamic scene optimization objectives to recover per-frame 3D geometry and camera parameters. Simultaneously, the correspondences lift 2D trajectories into smooth 3D trajectories, enabling fully integrated 4D reconstruction. Experiments show that our framework achieves complete 4D recovery and demonstrates strong performance across multiple downstream tasks, including depth estimation, camera pose estimation, and point tracking. Project Page: https://littlepure2333.github.io/C4D

Teaching robots to autonomously complete everyday tasks remains a challenge. Imitation Learning (IL) is a powerful approach that imbues robots with skills via demonstrations, but is limited by the labor-intensive process of collecting teleoperated robot data. Human videos offer a scalable alternative, but it remains difficult to directly train IL policies from them due to the lack of robot action labels. To address this, we propose to represent actions as short-horizon 2D trajectories on an image. These actions, or motion tracks, capture the predicted direction of motion for either human hands or robot end-effectors. We instantiate an IL policy called Motion Track Policy (MT-pi) which receives image observations and outputs motion tracks as actions. By leveraging this unified, cross-embodiment action space, MT-pi completes tasks with high success given just minutes of human video and limited additional robot demonstrations. At test time, we predict motion tracks from two camera views, recovering 6DoF trajectories via multi-view synthesis. MT-pi achieves an average success rate of 86.5% across 4 real-world tasks, outperforming state-of-the-art IL baselines which do not leverage human data or our action space by 40%, and generalizes to scenarios seen only in human videos. Code and videos are available on our website https://portal-cornell.github.io/motion_track_policy/.

Recent advancements in trajectory-guided video generation have achieved notable progress. However, existing models still face challenges in generating object motions with potentially changing 6D poses under wide-range rotations, due to limited 3D understanding. To address this problem, we introduce PoseTraj, a pose-aware video dragging model for generating 3D-aligned motion from 2D trajectories. Our method adopts a novel two-stage pose-aware pretraining framework, improving 3D understanding across diverse trajectories. Specifically, we propose a large-scale synthetic dataset PoseTraj-10K, containing 10k videos of objects following rotational trajectories, and enhance the model perception of object pose changes by incorporating 3D bounding boxes as intermediate supervision signals. Following this, we fine-tune the trajectory-controlling module on real-world videos, applying an additional camera-disentanglement module to further refine motion accuracy. Experiments on various benchmark datasets demonstrate that our method not only excels in 3D pose-aligned dragging for rotational trajectories but also outperforms existing baselines in trajectory accuracy and video quality.

Accurate depth estimation from monocular videos remains challenging due to ambiguities inherent in single-view geometry, as crucial depth cues like stereopsis are absent. However, humans often perceive relative depth intuitively by observing variations in the size and spacing of objects as they move. Inspired by this, we propose a novel method that infers relative depth by examining the spatial relationships and temporal evolution of a set of tracked 2D trajectories. Specifically, we use off-the-shelf point tracking models to capture 2D trajectories. Then, our approach employs spatial and temporal transformers to process these trajectories and directly infer depth changes over time. Evaluated on the TAPVid-3D benchmark, our method demonstrates robust zero-shot performance, generalizing effectively from synthetic to real-world datasets. Results indicate that our approach achieves temporally smooth, high-accuracy depth predictions across diverse domains.

Data scarcity continues to be a major challenge in the field of robotic manipulation. Although diffusion models provide a promising solution for generating robotic manipulation videos, existing methods largely depend on 2D trajectories, which inherently face issues with 3D spatial ambiguity. In this work, we present a novel framework named ManipDreamer3D for generating plausible 3D-aware robotic manipulation videos from the input image and the text instruction. Our method combines 3D trajectory planning with a reconstructed 3D occupancy map created from a third-person perspective, along with a novel trajectory-to-video diffusion model. Specifically, ManipDreamer3D first reconstructs the 3D occupancy representation from the input image and then computes an optimized 3D end-effector trajectory, minimizing path length while avoiding collisions. Next, we employ a latent editing technique to create video sequences from the initial image latent and the optimized 3D trajectory. This process conditions our specially trained trajectory-to-video diffusion model to produce robotic pick-and-place videos. Our method generates robotic videos with autonomously planned plausible 3D trajectories, significantly reducing human intervention requirements. Experimental results demonstrate superior visual quality compared to existing methods.

Deep learning approaches to natural language processing have made great strides in recent years. While these models produce symbols that convey vast amounts of diverse knowledge, it is unclear how such symbols are grounded in data from the world. In this paper, we explore the development of a private language for visual data representation by training emergent language (EL) encoders/decoders in both i) a traditional referential game environment and ii) a contrastive learning environment utilizing a within-class matching training paradigm. An additional classification layer utilizing neural machine translation and random forest classification was used to transform symbolic representations (sequences of integer symbols) to class labels. These methods were applied in two experiments focusing on object recognition and action recognition. For object recognition, a set of sketches produced by human participants from real imagery was used (Sketchy dataset) and for action recognition, 2D trajectories were generated from 3D motion capture systems (MOVI dataset). In order to interpret the symbols produced for data in each experiment, gradient-weighted class activation mapping (Grad-CAM) methods were used to identify pixel regions indicating semantic features which contribute evidence towards symbols in learned languages. Additionally, a t-distributed stochastic neighbor embedding (t-SNE) method was used to investigate embeddings learned by CNN feature extractors.

Analyzing a player's technique in table tennis requires knowledge of the ball's 3D trajectory and spin. While, the spin is not directly observable in standard broadcasting videos, we show that it can be inferred from the ball's trajectory in the video. We present a novel method to infer the initial spin and 3D trajectory from the corresponding 2D trajectory in a video. Without ground truth labels for broadcast videos, we train a neural network solely on synthetic data. Due to the choice of our input data representation, physically correct synthetic training data, and using targeted augmentations, the network naturally generalizes to real data. Notably, these simple techniques are sufficient to achieve generalization. No real data at all is required for training. To the best of our knowledge, we are the first to present a method for spin and trajectory prediction in simple monocular broadcast videos, achieving an accuracy of 92.0% in spin classification and a 2D reprojection error of 0.19% of the image diagonal.

This paper presents DriVerse, a generative model for simulating navigation-driven driving scenes from a single image and a future trajectory. Previous autonomous driving world models either directly feed the trajectory or discrete control signals into the generation pipeline, leading to poor alignment between the control inputs and the implicit features of the 2D base generative model, which results in low-fidelity video outputs. Some methods use coarse textual commands or discrete vehicle control signals, which lack the precision to guide fine-grained, trajectory-specific video generation, making them unsuitable for evaluating actual autonomous driving algorithms. DriVerse introduces explicit trajectory guidance in two complementary forms: it tokenizes trajectories into textual prompts using a predefined trend vocabulary for seamless language integration, and converts 3D trajectories into 2D spatial motion priors to enhance control over static content within the driving scene. To better handle dynamic objects, we further introduce a lightweight motion alignment module, which focuses on the inter-frame consistency of dynamic pixels, significantly enhancing the temporal coherence of moving elements over long sequences. With minimal training and no need for additional data, DriVerse outperforms specialized models on future video generation tasks across both the nuScenes and Waymo datasets. The code and models will be released to the public.

Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as-rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation.

Generative video editing has enabled several intuitive editing operations for short video clips that would previously have been difficult to achieve, especially for non-expert editors. Existing methods focus on prescribing an object's 3D or 2D motion trajectory in a video, or on altering the appearance of an object or a scene, while preserving both the video's plausibility and identity. Yet a method to move an object's 3D motion trajectory in a video, i.e., moving an object while preserving its relative 3D motion, is currently still missing. The main challenge lies in obtaining paired video data for this scenario. Previous methods typically rely on clever data generation approaches to construct plausible paired data from unpaired videos, but this approach fails if one of the videos in a pair can not easily be constructed from the other. Instead, we introduce TrajectoryAtlas, a new data generation pipeline for large-scale synthetic paired video data and a video generator TrajectoryMover fine-tuned with this data. We show that this successfully enables generative movement of object trajectories. Project page: https://chhatrekiran.github.io/trajectorymover

We present Text2Room, a method for generating room-scale textured 3D meshes from a given text prompt as input. To this end, we leverage pre-trained 2D text-to-image models to synthesize a sequence of images from different poses. In order to lift these outputs into a consistent 3D scene representation, we combine monocular depth estimation with a text-conditioned inpainting model. The core idea of our approach is a tailored viewpoint selection such that the content of each image can be fused into a seamless, textured 3D mesh. More specifically, we propose a continuous alignment strategy that iteratively fuses scene frames with the existing geometry to create a seamless mesh. Unlike existing works that focus on generating single objects or zoom-out trajectories from text, our method generates complete 3D scenes with multiple objects and explicit 3D geometry. We evaluate our approach using qualitative and quantitative metrics, demonstrating it as the first method to generate room-scale 3D geometry with compelling textures from only text as input.

Recent advancements in 3D object generation using diffusion models have achieved remarkable success, but generating realistic 3D urban scenes remains challenging. Existing methods relying solely on 3D diffusion models tend to suffer a degradation in appearance details, while those utilizing only 2D diffusion models typically compromise camera controllability. To overcome this limitation, we propose ScenDi, a method for urban scene generation that integrates both 3D and 2D diffusion models. We first train a 3D latent diffusion model to generate 3D Gaussians, enabling the rendering of images at a relatively low resolution. To enable controllable synthesis, this 3DGS generation process can be optionally conditioned by specifying inputs such as 3d bounding boxes, road maps, or text prompts. Then, we train a 2D video diffusion model to enhance appearance details conditioned on rendered images from the 3D Gaussians. By leveraging the coarse 3D scene as guidance for 2D video diffusion, ScenDi generates desired scenes based on input conditions and successfully adheres to accurate camera trajectories. Experiments on two challenging real-world datasets, Waymo and KITTI-360, demonstrate the effectiveness of our approach.

This paper addresses the challenge of learning semantically and functionally meaningful 3D motion priors from real-world videos, in order to enable prediction of future 3D scene motion from a single input image. We propose a novel pixel-aligned Motion Map (MoMap) representation for 3D scene motion, which can be generated from existing generative image models to facilitate efficient and effective motion prediction. To learn meaningful distributions over motion, we create a large-scale database of MoMaps from over 50,000 real videos and train a diffusion model on these representations. Our motion generation not only synthesizes trajectories in 3D but also suggests a new pipeline for 2D video synthesis: first generate a MoMap, then warp an image accordingly and complete the warped point-based renderings. Experimental results demonstrate that our approach generates plausible and semantically consistent 3D scene motion.

View-predictive generative models provide strong priors for lifting object-centric images and videos into 3D and 4D through rendering and score distillation objectives. A question then remains: what about lifting complete multi-object dynamic scenes? There are two challenges in this direction: First, rendering error gradients are often insufficient to recover fast object motion, and second, view predictive generative models work much better for objects than whole scenes, so, score distillation objectives cannot currently be applied at the scene level directly. We present DreamScene4D, the first approach to generate 3D dynamic scenes of multiple objects from monocular videos via 360-degree novel view synthesis. Our key insight is a "decompose-recompose" approach that factorizes the video scene into the background and object tracks, while also factorizing object motion into 3 components: object-centric deformation, object-to-world-frame transformation, and camera motion. Such decomposition permits rendering error gradients and object view-predictive models to recover object 3D completions and deformations while bounding box tracks guide the large object movements in the scene. We show extensive results on challenging DAVIS, Kubric, and self-captured videos with quantitative comparisons and a user preference study. Besides 4D scene generation, DreamScene4D obtains accurate 2D persistent point track by projecting the inferred 3D trajectories to 2D. We will release our code and hope our work will stimulate more research on fine-grained 4D understanding from videos.

Generating immersive 3D scenes from texts is a core task in computer vision, crucial for applications in virtual reality and game development. Despite the promise of leveraging 2D diffusion priors, existing methods suffer from spatial blindness and rely on predefined trajectories that fail to exploit the inner relationships among salient objects. Consequently, these approaches are unable to comprehend the semantic layout, preventing them from exploring the scene adaptively to infer occluded content. Moreover, current inpainting models operate in 2D image space, struggling to plausibly fill holes caused by camera motion. To address these limitations, we propose RoamScene3D, a novel framework that bridges the gap between semantic guidance and spatial generation. Our method reasons about the semantic relations among objects and produces consistent and photorealistic scenes. Specifically, we employ a vision-language model (VLM) to construct a scene graph that encodes object relations, guiding the camera to perceive salient object boundaries and plan an adaptive roaming trajectory. Furthermore, to mitigate the limitations of static 2D priors, we introduce a Motion-Injected Inpainting model that is fine-tuned on a synthetic panoramic dataset integrating authentic camera trajectories, making it adaptive to camera motion. Extensive experiments demonstrate that with semantic reasoning and geometric constraints, our method significantly outperforms state-of-the-art approaches in producing consistent and photorealistic scenes. Our code is available at https://github.com/JS-CHU/RoamScene3D.

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.

We introduce 4DGS360, a diffusion-free framework for 360^{circ} dynamic object reconstruction from casual monocular video. Existing methods often fail to reconstruct consistent 360^{circ} geometry, as their heavy reliance on 2D-native priors causes initial points to overfit to visible surface in each training view. 4DGS360 addresses this challenge through a advanced 3D-native initialization that mitigates the geometric ambiguity of occluded regions. Our proposed 3D tracker, AnchorTAP3D, produces reinforced 3D point trajectories by leveraging confident 2D track points as anchors, suppressing drift and providing reliable initialization that preserves geometry in occluded regions. This initialization, combined with optimization, yields coherent 360^{circ} 4D reconstructions. We further present iPhone360, a new benchmark where test cameras are placed up to 135^{circ} apart from training views, enabling 360^{circ} evaluation that existing datasets cannot provide. Experiments show that 4DGS360 achieves state-of-the-art performance on the iPhone360, iPhone, and DAVIS datasets, both qualitatively and quantitatively.

Monocular 3D tracking aims to capture the long-term motion of pixels in 3D space from a single monocular video and has witnessed rapid progress in recent years. However, we argue that the existing monocular 3D tracking methods still fall short in separating the camera motion from foreground dynamic motion and cannot densely track newly emerging dynamic subjects in the videos. To address these two limitations, we propose TrackingWorld, a novel pipeline for dense 3D tracking of almost all pixels within a world-centric 3D coordinate system. First, we introduce a tracking upsampler that efficiently lifts the arbitrary sparse 2D tracks into dense 2D tracks. Then, to generalize the current tracking methods to newly emerging objects, we apply the upsampler to all frames and reduce the redundancy of 2D tracks by eliminating the tracks in overlapped regions. Finally, we present an efficient optimization-based framework to back-project dense 2D tracks into world-centric 3D trajectories by estimating the camera poses and the 3D coordinates of these 2D tracks. Extensive evaluations on both synthetic and real-world datasets demonstrate that our system achieves accurate and dense 3D tracking in a world-centric coordinate frame.

Unsupervised learning of object-centric representations in dynamic visual scenes is challenging. Unlike most previous approaches that learn to decompose 2D images, we present DynaVol, a 3D scene generative model that unifies geometric structures and object-centric learning in a differentiable volume rendering framework. The key idea is to perform object-centric voxelization to capture the 3D nature of the scene, which infers the probability distribution over objects at individual spatial locations. These voxel features evolve over time through a canonical-space deformation function, forming the basis for global representation learning via slot attention. The voxel features and global features are complementary and are both leveraged by a compositional NeRF decoder for volume rendering. DynaVol remarkably outperforms existing approaches for unsupervised dynamic scene decomposition. Once trained, the explicitly meaningful voxel features enable additional capabilities that 2D scene decomposition methods cannot achieve: it is possible to freely edit the geometric shapes or manipulate the motion trajectories of the objects.

Current Visual-Language Navigation (VLN) methodologies face a trade-off between semantic understanding and control precision. While Multimodal Large Language Models (MLLMs) offer superior reasoning, deploying them as low-level controllers leads to high latency, trajectory oscillations, and poor generalization due to weak geometric grounding. To address these limitations, we propose Fly0, a framework that decouples semantic reasoning from geometric planning. The proposed method operates through a three-stage pipeline: (1) an MLLM-driven module for grounding natural language instructions into 2D pixel coordinates; (2) a geometric projection module that utilizes depth data to localize targets in 3D space; and (3) a geometric planner that generates collision-free trajectories. This mechanism enables robust navigation even when visual contact is lost. By eliminating the need for continuous inference, Fly0 reduces computational overhead and improves system stability. Extensive experiments in simulation and real-world environments demonstrate that Fly0 outperforms state-of-the-art baselines, improving the Success Rate by over 20\% and reducing Navigation Error (NE) by approximately 50\% in unstructured environments. Our code is available at https://github.com/xuzhenxing1/Fly0.

Modern generative video models excel at producing convincing, high-quality outputs, but struggle to maintain multi-view and spatiotemporal consistency in highly dynamic real-world environments. In this work, we introduce AnyView, a diffusion-based video generation framework for dynamic view synthesis with minimal inductive biases or geometric assumptions. We leverage multiple data sources with various levels of supervision, including monocular (2D), multi-view static (3D) and multi-view dynamic (4D) datasets, to train a generalist spatiotemporal implicit representation capable of producing zero-shot novel videos from arbitrary camera locations and trajectories. We evaluate AnyView on standard benchmarks, showing competitive results with the current state of the art, and propose AnyViewBench, a challenging new benchmark tailored towards extreme dynamic view synthesis in diverse real-world scenarios. In this more dramatic setting, we find that most baselines drastically degrade in performance, as they require significant overlap between viewpoints, while AnyView maintains the ability to produce realistic, plausible, and spatiotemporally consistent videos when prompted from any viewpoint. Results, data, code, and models can be viewed at: https://tri-ml.github.io/AnyView/

We introduce TAPIP3D, a novel approach for long-term 3D point tracking in monocular RGB and RGB-D videos. TAPIP3D represents videos as camera-stabilized spatio-temporal feature clouds, leveraging depth and camera motion information to lift 2D video features into a 3D world space where camera motion is effectively canceled. TAPIP3D iteratively refines multi-frame 3D motion estimates within this stabilized representation, enabling robust tracking over extended periods. To manage the inherent irregularities of 3D point distributions, we propose a Local Pair Attention mechanism. This 3D contextualization strategy effectively exploits spatial relationships in 3D, forming informative feature neighborhoods for precise 3D trajectory estimation. Our 3D-centric approach significantly outperforms existing 3D point tracking methods and even enhances 2D tracking accuracy compared to conventional 2D pixel trackers when accurate depth is available. It supports inference in both camera coordinates (i.e., unstabilized) and world coordinates, and our results demonstrate that compensating for camera motion improves tracking performance. Our approach replaces the conventional 2D square correlation neighborhoods used in prior 2D and 3D trackers, leading to more robust and accurate results across various 3D point tracking benchmarks. Project Page: https://tapip3d.github.io

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image generation has the following properties: (i) individual trajectories tend to be low-dimensional and resemble 2D `rotations'; (ii) high-variance scene features like layout tend to emerge earlier, while low-variance details tend to emerge later; and (iii) early perturbations tend to have a greater impact on image content than later perturbations. To understand these phenomena, we derive and study a closed-form solution to the probability flow ODE for a Gaussian distribution, which shows that the reverse diffusion state rotates towards a gradually-specified target on the image manifold. It also shows that generation involves first committing to an outline, and then to finer and finer details. We find that this solution accurately describes the initial phase of image generation for pretrained models, and can in principle be used to make image generation more efficient by skipping reverse diffusion steps. Finally, we use our solution to characterize the image manifold in Stable Diffusion. Our viewpoint reveals an unexpected similarity between generation by GANs and diffusion and provides a conceptual link between diffusion and image retrieval.

3D scene generation has long been dominated by 2D multi-view or video diffusion models. This is due not only to the lack of scene-level 3D latent representation, but also to the fact that most scene-level 3D visual data exists in the form of multi-view images or videos, which are naturally compatible with 2D diffusion architectures. Typically, these 2D-based approaches degrade 3D spatial extrapolation to 2D temporal extension, which introduces two fundamental issues: (i) representing 3D scenes via 2D views leads to significant representation redundancy, and (ii) latent space rooted in 2D inherently limits the spatial consistency of the generated 3D scenes. In this paper, we propose, for the first time, to perform 3D scene generation directly within an implicit 3D latent space to address these limitations. First, we repurpose frozen 2D representation encoders to construct our 3D Representation Autoencoder (3DRAE), which grounds view-coupled 2D semantic representations into a view-decoupled 3D latent representation. This enables representing 3D scenes observed from arbitrary numbers of views--at any resolution and aspect ratio--with fixed complexity and rich semantics. Then we introduce 3D Diffusion Transformer (3DDiT), which performs diffusion modeling in this 3D latent space, achieving remarkably efficient and spatially consistent 3D scene generation while supporting diverse conditioning configurations. Moreover, since our approach directly generates a 3D scene representation, it can be decoded to images and optional point maps along arbitrary camera trajectories without requiring per-trajectory diffusion sampling pass, which is common in 2D-based approaches.

The field of trajectory forecasting has grown significantly in recent years, partially owing to the release of numerous large-scale, real-world human trajectory datasets for autonomous vehicles (AVs) and pedestrian motion tracking. While such datasets have been a boon for the community, they each use custom and unique data formats and APIs, making it cumbersome for researchers to train and evaluate methods across multiple datasets. To remedy this, we present trajdata: a unified interface to multiple human trajectory datasets. At its core, trajdata provides a simple, uniform, and efficient representation and API for trajectory and map data. As a demonstration of its capabilities, in this work we conduct a comprehensive empirical evaluation of existing trajectory datasets, providing users with a rich understanding of the data underpinning much of current pedestrian and AV motion forecasting research, and proposing suggestions for future datasets from these insights. trajdata is permissively licensed (Apache 2.0) and can be accessed online at https://github.com/NVlabs/trajdata

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of them (such as finding their intersections) can be done offline. At runtime we quickly generate a smooth path between given initial and terminal positions. Our algorithm designs trajectories that are guaranteed to be safe at all times, and detects infeasibility whenever such a trajectory does not exist. Our algorithm is based on two subproblems that we can solve very efficiently: finding a shortest path in a weighted graph, and solving (multiple) convex optimal-control problems. We demonstrate the proposed path planner on large-scale numerical examples, and we provide an efficient open-source software implementation, fastpathplanning.

We present a novel data-driven simulation environment for modeling traffic in metropolitan street intersections. Using real-world tracking data collected over an extended period of time, we train trajectory forecasting models to learn agent interactions and environmental constraints that are difficult to capture conventionally. Trajectories of new agents are first coarsely generated by sampling from the spatial and temporal generative distributions, then refined using state-of-the-art trajectory forecasting models. The simulation can run either autonomously, or under explicit human control conditioned on the generative distributions. We present the experiments for a variety of model configurations. Under an iterative prediction scheme, the way-point-supervised TrajNet++ model obtained 0.36 Final Displacement Error (FDE) in 20 FPS on an NVIDIA A100 GPU.

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

Flight trajectory data plays a vital role in the traffic management community, especially for downstream tasks such as trajectory prediction, flight recognition, and anomaly detection. Existing works often utilize handcrafted features and design models for different tasks individually, which heavily rely on domain expertise and are hard to extend. We argue that different flight analysis tasks share the same useful features of the trajectory. Jointly learning a unified representation for flight trajectories could be beneficial for improving the performance of various tasks. However, flight trajectory representation learning (TRL) faces two primary challenges, \ie unbalanced behavior density and 3D spatial continuity, which disable recent general TRL methods. In this paper, we propose Flight2Vec , a flight-specific representation learning method to address these challenges. Specifically, a behavior-adaptive patching mechanism is used to inspire the learned representation to pay more attention to behavior-dense segments. Moreover, we introduce a motion trend learning technique that guides the model to memorize not only the precise locations, but also the motion trend to generate better representations. Extensive experimental results demonstrate that Flight2Vec significantly improves performance in downstream tasks such as flight trajectory prediction, flight recognition, and anomaly detection.

User profiling and region analysis are two tasks of significant commercial value. However, in practical applications, modeling different features typically involves four main steps: data preparation, data processing, model establishment, evaluation, and optimization. This process is time-consuming and labor-intensive. Repeating this workflow for each feature results in abundant development time for tasks and a reduced overall volume of task development. Indeed, human mobility data contains a wealth of information. Several successful cases suggest that conducting in-depth analysis of population movement data could potentially yield meaningful profiles about users and areas. Nonetheless, most related works have not thoroughly utilized the semantic information within human mobility data and trained on a fixed number of the regions. To tap into the rich information within population movement, based on the perspective that Regions Are Who walk them, we propose a large spatiotemporal model based on trajectories (RAW). It possesses the following characteristics: 1) Tailored for trajectory data, introducing a GPT-like structure with a parameter count of up to 1B; 2) Introducing a spatiotemporal fine-tuning module, interpreting trajectories as collection of users to derive arbitrary region embedding. This framework allows rapid task development based on the large spatiotemporal model. We conducted extensive experiments to validate the effectiveness of our proposed large spatiotemporal model. It's evident that our proposed method, relying solely on human mobility data without additional features, exhibits a certain level of relevance in user profiling and region analysis. Moreover, our model showcases promising predictive capabilities in trajectory generation tasks based on the current state, offering the potential for further innovative work utilizing this large spatiotemporal model.

Predicting future motion is crucial in video understanding and controllable video generation. Dense point trajectories are a compact, expressive motion representation, but modeling their future evolution from observed video remains challenging. We propose a framework that predicts future trajectories and visibility from past trajectories and video context. Our method has three components: (1) Grid-Anchor Offset Encoding, which reduces location-dependent bias by representing each point as an offset from its pixel-center anchor; (2) TrajLoom-VAE, which learns a compact spatiotemporal latent space for dense trajectories with masked reconstruction and a spatiotemporal consistency regularizer; and (3) TrajLoom-Flow, which generates future trajectories in latent space via flow matching, with boundary cues and on-policy K-step fine-tuning for stable sampling. We also introduce TrajLoomBench, a unified benchmark spanning real and synthetic videos with a standardized setup aligned with video-generation benchmarks. Compared with state-of-the-art methods, our approach extends the prediction horizon from 24 to 81 frames while improving motion realism and stability across datasets. The predicted trajectories directly support downstream video generation and editing. Code, model checkpoints, and datasets are available at https://trajloom.github.io/.

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

Effective spatio-temporal representation is fundamental to modeling, understanding, and predicting dynamics in videos. The atomic unit of a video, the pixel, traces a continuous 3D trajectory over time, serving as the primitive element of dynamics. Based on this principle, we propose representing any video as a Trajectory Field: a dense mapping that assigns a continuous 3D trajectory function of time to each pixel in every frame. With this representation, we introduce Trace Anything, a neural network that predicts the entire trajectory field in a single feed-forward pass. Specifically, for each pixel in each frame, our model predicts a set of control points that parameterizes a trajectory (i.e., a B-spline), yielding its 3D position at arbitrary query time instants. We trained the Trace Anything model on large-scale 4D data, including data from our new platform, and our experiments demonstrate that: (i) Trace Anything achieves state-of-the-art performance on our new benchmark for trajectory field estimation and performs competitively on established point-tracking benchmarks; (ii) it offers significant efficiency gains thanks to its one-pass paradigm, without requiring iterative optimization or auxiliary estimators; and (iii) it exhibits emergent abilities, including goal-conditioned manipulation, motion forecasting, and spatio-temporal fusion. Project page: https://trace-anything.github.io/.

Efficient and accurate motion prediction is crucial for ensuring safety and informed decision-making in autonomous driving, particularly under dynamic real-world conditions that necessitate multi-modal forecasts. We introduce TrajFlow, a novel flow matching-based motion prediction framework that addresses the scalability and efficiency challenges of existing generative trajectory prediction methods. Unlike conventional generative approaches that employ i.i.d. sampling and require multiple inference passes to capture diverse outcomes, TrajFlow predicts multiple plausible future trajectories in a single pass, significantly reducing computational overhead while maintaining coherence across predictions. Moreover, we propose a ranking loss based on the Plackett-Luce distribution to improve uncertainty estimation of predicted trajectories. Additionally, we design a self-conditioning training technique that reuses the model's own predictions to construct noisy inputs during a second forward pass, thereby improving generalization and accelerating inference. Extensive experiments on the large-scale Waymo Open Motion Dataset (WOMD) demonstrate that TrajFlow achieves state-of-the-art performance across various key metrics, underscoring its effectiveness for safety-critical autonomous driving applications. The code and other details are available on the project website https://traj-flow.github.io/.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

We consider the problem of forecasting motion from a single image, i.e., predicting how objects in the world are likely to move, without the ability to observe other parameters such as the object velocities or the forces applied to them. We formulate this task as conditional generation of dense trajectory grids with a model that closely follows the architecture of modern video generators but outputs motion trajectories instead of pixels. This approach captures scene-wide dynamics and uncertainty, yielding more accurate and diverse predictions than prior regressors and generators. We extensively evaluate our method on simulated data, demonstrate its effectiveness on downstream applications such as robotics, and show promising accuracy on real-world intuitive physics datasets. Although recent state-of-the-art video generators are often regarded as world models, we show that they struggle with forecasting motion from a single image, even in simple physical scenarios such as falling blocks or mechanical object interactions, despite fine-tuning on such data. We show that this limitation arises from the overhead of generating pixels rather than directly modeling motion.

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 extend the reconstruct-then-generate framework to jointly perform Motion generation and geometric Reconstruction for 4D Synthesis (MoRe4D). We first introduce TrajScene-60K, a large-scale dataset of 60,000 video samples with dense point trajectories, addressing the scarcity of high-quality 4D scene data. Based on this, we propose a diffusion-based 4D Scene Trajectory Generator (4D-STraG) to jointly generate geometrically consistent and motion-plausible 4D point trajectories. To leverage single-view priors, we design a depth-guided motion normalization strategy and a motion-aware module for effective geometry and dynamics integration. We then propose a 4D View Synthesis Module (4D-ViSM) to render videos with arbitrary camera trajectories from 4D point track representations. Experiments show that MoRe4D generates high-quality 4D scenes with multi-view consistency and rich dynamic details from a single image. Code: https://github.com/Zhangyr2022/MoRe4D.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Human trajectory prediction is a practical task of predicting the future positions of pedestrians on the road, which typically covers all temporal ranges from short-term to long-term within a trajectory. However, existing works attempt to address the entire trajectory prediction with a singular, uniform training paradigm, neglecting the distinction between short-term and long-term dynamics in human trajectories. To overcome this limitation, we introduce a novel Progressive Pretext Task learning (PPT) framework, which progressively enhances the model's capacity of capturing short-term dynamics and long-term dependencies for the final entire trajectory prediction. Specifically, we elaborately design three stages of training tasks in the PPT framework. In the first stage, the model learns to comprehend the short-term dynamics through a stepwise next-position prediction task. In the second stage, the model is further enhanced to understand long-term dependencies through a destination prediction task. In the final stage, the model aims to address the entire future trajectory task by taking full advantage of the knowledge from previous stages. To alleviate the knowledge forgetting, we further apply a cross-task knowledge distillation. Additionally, we design a Transformer-based trajectory predictor, which is able to achieve highly efficient two-step reasoning by integrating a destination-driven prediction strategy and a group of learnable prompt embeddings. Extensive experiments on popular benchmarks have demonstrated that our proposed approach achieves state-of-the-art performance with high efficiency. Code is available at https://github.com/iSEE-Laboratory/PPT.

Text-driven human motion synthesis is capturing significant attention for its ability to effortlessly generate intricate movements from abstract text cues, showcasing its potential for revolutionizing motion design not only in film narratives but also in virtual reality experiences and computer game development. Existing methods often rely on 3D motion capture data, which require special setups resulting in higher costs for data acquisition, ultimately limiting the diversity and scope of human motion. In contrast, 2D human videos offer a vast and accessible source of motion data, covering a wider range of styles and activities. In this paper, we explore leveraging 2D human motion extracted from videos as an alternative data source to improve text-driven 3D motion generation. Our approach introduces a novel framework that disentangles local joint motion from global movements, enabling efficient learning of local motion priors from 2D data. We first train a single-view 2D local motion generator on a large dataset of text-motion pairs. To enhance this model to synthesize 3D motion, we fine-tune the generator with 3D data, transforming it into a multi-view generator that predicts view-consistent local joint motion and root dynamics. Experiments on the HumanML3D dataset and novel text prompts demonstrate that our method efficiently utilizes 2D data, supporting realistic 3D human motion generation and broadening the range of motion types it supports. Our code will be made publicly available at https://zju3dv.github.io/Motion-2-to-3/.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

Diffusion models operate in a reflexive System 1 mode, constrained by a fixed, content-agnostic sampling schedule. This rigidity arises from the curse of state dimensionality, where the combinatorial explosion of possible states in the high-dimensional noise manifold renders explicit trajectory planning intractable and leads to systematic computational misallocation. To address this, we introduce Chain-of-Trajectories (CoTj), a train-free framework enabling System 2 deliberative planning. Central to CoTj is Diffusion DNA, a low-dimensional signature that quantifies per-stage denoising difficulty and serves as a proxy for the high-dimensional state space, allowing us to reformulate sampling as graph planning on a directed acyclic graph. Through a Predict-Plan-Execute paradigm, CoTj dynamically allocates computational effort to the most challenging generative phases. Experiments across multiple generative models demonstrate that CoTj discovers context-aware trajectories, improving output quality and stability while reducing redundant computation. This work establishes a new foundation for resource-aware, planning-based diffusion modeling. The code is available at https://github.com/UnicomAI/CoTj.

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

Natural agents can effectively learn from multiple data sources that differ in size, quality, and types of measurements. We study this heterogeneity in the context of offline reinforcement learning (RL) by introducing a new, practically motivated semi-supervised setting. Here, an agent has access to two sets of trajectories: labelled trajectories containing state, action and reward triplets at every timestep, along with unlabelled trajectories that contain only state and reward information. For this setting, we develop and study a simple meta-algorithmic pipeline that learns an inverse dynamics model on the labelled data to obtain proxy-labels for the unlabelled data, followed by the use of any offline RL algorithm on the true and proxy-labelled trajectories. Empirically, we find this simple pipeline to be highly successful -- on several D4RL benchmarks~fu2020d4rl, certain offline RL algorithms can match the performance of variants trained on a fully labelled dataset even when we label only 10\% of trajectories which are highly suboptimal. To strengthen our understanding, we perform a large-scale controlled empirical study investigating the interplay of data-centric properties of the labelled and unlabelled datasets, with algorithmic design choices (e.g., choice of inverse dynamics, offline RL algorithm) to identify general trends and best practices for training RL agents on semi-supervised offline datasets.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

There are five types of trajectory prediction tasks: deterministic, stochastic, domain adaptation, momentary observation, and few-shot. These associated tasks are defined by various factors, such as the length of input paths, data split and pre-processing methods. Interestingly, even though they commonly take sequential coordinates of observations as input and infer future paths in the same coordinates as output, designing specialized architectures for each task is still necessary. For the other task, generality issues can lead to sub-optimal performances. In this paper, we propose SingularTrajectory, a diffusion-based universal trajectory prediction framework to reduce the performance gap across the five tasks. The core of SingularTrajectory is to unify a variety of human dynamics representations on the associated tasks. To do this, we first build a Singular space to project all types of motion patterns from each task into one embedding space. We next propose an adaptive anchor working in the Singular space. Unlike traditional fixed anchor methods that sometimes yield unacceptable paths, our adaptive anchor enables correct anchors, which are put into a wrong location, based on a traversability map. Finally, we adopt a diffusion-based predictor to further enhance the prototype paths using a cascaded denoising process. Our unified framework ensures the generality across various benchmark settings such as input modality, and trajectory lengths. Extensive experiments on five public benchmarks demonstrate that SingularTrajectory substantially outperforms existing models, highlighting its effectiveness in estimating general dynamics of human movements. Code is publicly available at https://github.com/inhwanbae/SingularTrajectory .

We present a novel model for Tracking Any Point (TAP) that effectively tracks any queried point on any physical surface throughout a video sequence. Our approach employs two stages: (1) a matching stage, which independently locates a suitable candidate point match for the query point on every other frame, and (2) a refinement stage, which updates both the trajectory and query features based on local correlations. The resulting model surpasses all baseline methods by a significant margin on the TAP-Vid benchmark, as demonstrated by an approximate 20% absolute average Jaccard (AJ) improvement on DAVIS. Our model facilitates fast inference on long and high-resolution video sequences. On a modern GPU, our implementation has the capacity to track points faster than real-time, and can be flexibly extended to higher-resolution videos. Given the high-quality trajectories extracted from a large dataset, we demonstrate a proof-of-concept diffusion model which generates trajectories from static images, enabling plausible animations. Visualizations, source code, and pretrained models can be found on our project webpage.

Recent advances in large language models (LLMs) have sparked growing interest in integrating language-driven techniques into trajectory prediction. By leveraging their semantic and reasoning capabilities, LLMs are reshaping how autonomous systems perceive, model, and predict trajectories. This survey provides a comprehensive overview of this emerging field, categorizing recent work into five directions: (1) Trajectory prediction via language modeling paradigms, (2) Direct trajectory prediction with pretrained language models, (3) Language-guided scene understanding for trajectory prediction, (4) Language-driven data generation for trajectory prediction, (5) Language-based reasoning and interpretability for trajectory prediction. For each, we analyze representative methods, highlight core design choices, and identify open challenges. This survey bridges natural language processing and trajectory prediction, offering a unified perspective on how language can enrich trajectory prediction.

We present a novel approach for generating motion primitives for kinodynamic motion planning using diffusion models. The motions generated by our approach are adapted to each problem instance by utilizing problem-specific parameters, allowing for finding solutions faster and of better quality. The diffusion models used in our approach are trained on randomly cut solution trajectories. These trajectories are created by solving randomly generated problem instances with a kinodynamic motion planner. Experimental results show significant improvements up to 30 percent in both computation time and solution quality across varying robot dynamics such as second-order unicycle or car with trailer.

This work investigates the reproducibility of the paper 'Explaining RL decisions with trajectories'. The original paper introduces a novel approach in explainable reinforcement learning based on the attribution decisions of an agent to specific clusters of trajectories encountered during training. We verify the main claims from the paper, which state that (i) training on less trajectories induces a lower initial state value, (ii) trajectories in a cluster present similar high-level patterns, (iii) distant trajectories influence the decision of an agent, and (iv) humans correctly identify the attributed trajectories to the decision of the agent. We recover the environments used by the authors based on the partial original code they provided for one of the environments (Grid-World), and implemented the remaining from scratch (Seaquest, HalfCheetah, Breakout and Q*Bert). While we confirm that (i), (ii), and (iii) partially hold, we extend on the largely qualitative experiments from the authors by introducing a quantitative metric to further support (iii), and new experiments and visual results for (i). Moreover, we investigate the use of different clustering algorithms and encoder architectures to further support (ii). We could not support (iv), given the limited extent of the original experiments. We conclude that, while some of the claims can be supported, further investigations and experiments could be of interest. We recognise the novelty of the work from the authors and hope that our work paves the way for clearer and more transparent approaches.

Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous differential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization problem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of Bézier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap rounding of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

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 present an approach to modeling an image-space prior on scene dynamics. Our prior is learned from a collection of motion trajectories extracted from real video sequences containing natural, oscillating motion such as trees, flowers, candles, and clothes blowing in the wind. Given a single image, our trained model uses a frequency-coordinated diffusion sampling process to predict a per-pixel long-term motion representation in the Fourier domain, which we call a neural stochastic motion texture. This representation can be converted into dense motion trajectories that span an entire video. Along with an image-based rendering module, these trajectories can be used for a number of downstream applications, such as turning still images into seamlessly looping dynamic videos, or allowing users to realistically interact with objects in real pictures.

Mobile devices continuously interact with cellular base stations, generating massive volumes of signaling records that provide broad coverage for understanding human mobility. However, such records offer only coarse location cues (e.g., serving-cell identifiers) and therefore limit their direct use in applications that require high-precision GPS trajectories. This paper studies the Sig2GPS problem: reconstructing GPS trajectories from cellular signaling. Inspired by domain experts often lay the signaling trace on the map and sketch the corresponding GPS route, unlike conventional solutions that rely on complex multi-stage engineering pipelines or regress coordinates, Sig2GPS is reframed as an image-to-video generation task that directly operates in the map-visual domain: signaling traces are rendered on a map, and a video generation model is trained to draw a continuous GPS path. To support this paradigm, a paired signaling-to-trajectory video dataset is constructed to fine-tune an open-source video model, and a trajectory-aware reinforcement learning-based optimization method is introduced to improve generation fidelity via rewards. Experiments on large-scale real-world datasets show substantial improvements over strong engineered and learning-based baselines, while additional results on next GPS prediction indicate scalability and cross-city transferability. Overall, these results suggest that map-visual video generation provides a practical interface for trajectory data mining by enabling direct generation and refinement of continuous paths under map constraints.

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research challenge. Most prior work has aimed to solve this challenge by modeling latent structures linearly, and finding corresponding linear directions which result in `disentangled' generations. In this work, we instead propose to model latent structures with a learned dynamic potential landscape, thereby performing latent traversals as the flow of samples down the landscape's gradient. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations, thereby allowing them to flexibly vary over both space and time. To achieve disentanglement, multiple potentials are learned simultaneously, and are constrained by a classifier to be distinct and semantically self-consistent. Experimentally, we demonstrate that our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines. Further, we demonstrate that our method can be integrated as a regularization term during training, thereby acting as an inductive bias towards the learning of structured representations, ultimately improving model likelihood on similarly structured data.

Next point-of-interest (POI) recommendation predicts a user's next destination from historical movements. Traditional models require intensive training, while LLMs offer flexible and generalizable zero-shot solutions but often generate generic or geographically irrelevant results due to missing trajectory and spatial context. To address these issues, we propose RALLM-POI, a framework that couples LLMs with retrieval-augmented generation and self-rectification. We first propose a Historical Trajectory Retriever (HTR) that retrieves relevant past trajectories to serve as contextual references, which are then reranked by a Geographical Distance Reranker (GDR) for prioritizing spatially relevant trajectories. Lastly, an Agentic LLM Rectifier (ALR) is designed to refine outputs through self-reflection. Without additional training, RALLM-POI achieves substantial accuracy gains across three real-world Foursquare datasets, outperforming both conventional and LLM-based baselines. Code is released at https://github.com/LKRcrocodile/RALLM-POI.

Recent work has demonstrated the effectiveness of formulating decision making as a supervised learning problem on offline-collected trajectories. However, the benefits of performing sequence modeling on trajectory data is not yet clear. In this work we investigate if sequence modeling has the capability to condense trajectories into useful representations that can contribute to policy learning. To achieve this, we adopt a two-stage framework that first summarizes trajectories with sequence modeling techniques, and then employs these representations to learn a policy along with a desired goal. This design allows many existing supervised offline RL methods to be considered as specific instances of our framework. Within this framework, we introduce Goal-Conditioned Predicitve Coding (GCPC), an approach that brings powerful trajectory representations and leads to performant policies. We conduct extensive empirical evaluations on AntMaze, FrankaKitchen and Locomotion environments, and observe that sequence modeling has a significant impact on some decision making tasks. In addition, we demonstrate that GCPC learns a goal-conditioned latent representation about the future, which serves as an "implicit planner", and enables competitive performance on all three benchmarks.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

We introduce Masked Trajectory Models (MTM) as a generic abstraction for sequential decision making. MTM takes a trajectory, such as a state-action sequence, and aims to reconstruct the trajectory conditioned on random subsets of the same trajectory. By training with a highly randomized masking pattern, MTM learns versatile networks that can take on different roles or capabilities, by simply choosing appropriate masks at inference time. For example, the same MTM network can be used as a forward dynamics model, inverse dynamics model, or even an offline RL agent. Through extensive experiments in several continuous control tasks, we show that the same MTM network -- i.e. same weights -- can match or outperform specialized networks trained for the aforementioned capabilities. Additionally, we find that state representations learned by MTM can significantly accelerate the learning speed of traditional RL algorithms. Finally, in offline RL benchmarks, we find that MTM is competitive with specialized offline RL algorithms, despite MTM being a generic self-supervised learning method without any explicit RL components. Code is available at https://github.com/facebookresearch/mtm

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.

Dynamic objects in our physical 4D (3D + time) world are constantly evolving, deforming, and interacting with other objects, leading to diverse 4D scene dynamics. In this paper, we present a universal generative pipeline, CHORD, for CHOReographing Dynamic objects and scenes and synthesizing this type of phenomena. Traditional rule-based graphics pipelines to create these dynamics are based on category-specific heuristics, yet are labor-intensive and not scalable. Recent learning-based methods typically demand large-scale datasets, which may not cover all object categories in interest. Our approach instead inherits the universality from the video generative models by proposing a distillation-based pipeline to extract the rich Lagrangian motion information hidden in the Eulerian representations of 2D videos. Our method is universal, versatile, and category-agnostic. We demonstrate its effectiveness by conducting experiments to generate a diverse range of multi-body 4D dynamics, show its advantage compared to existing methods, and demonstrate its applicability in generating robotics manipulation policies. Project page: https://yanzhelyu.github.io/chord

We present a multi-modal trajectory generation and selection algorithm for real-world mapless outdoor navigation in human-centered environments. Such environments contain rich features like crosswalks, grass, and curbs, which are easily interpretable by humans, but not by mobile robots. We aim to compute suitable trajectories that (1) satisfy the environment-specific traversability constraints and (2) generate human-like paths while navigating on crosswalks, sidewalks, etc. Our formulation uses a Conditional Variational Autoencoder (CVAE) generative model enhanced with traversability constraints to generate multiple candidate trajectories for global navigation. We develop a visual prompting approach and leverage the Visual Language Model's (VLM) zero-shot ability of semantic understanding and logical reasoning to choose the best trajectory given the contextual information about the task. We evaluate our method in various outdoor scenes with wheeled robots and compare the performance with other global navigation algorithms. In practice, we observe an average improvement of 20.81% in satisfying traversability constraints and 28.51% in terms of human-like navigation in four different outdoor navigation scenarios.

Trajectory generation has garnered significant attention from researchers in the field of spatio-temporal analysis, as it can generate substantial synthesized human mobility trajectories that enhance user privacy and alleviate data scarcity. However, existing trajectory generation methods often focus on improving trajectory generation quality from a singular perspective, lacking a comprehensive semantic understanding across various scales. Consequently, we are inspired to develop a HOlistic SEmantic Representation (HOSER) framework for navigational trajectory generation. Given an origin-and-destination (OD) pair and the starting time point of a latent trajectory, we first propose a Road Network Encoder to expand the receptive field of road- and zone-level semantics. Second, we design a Multi-Granularity Trajectory Encoder to integrate the spatio-temporal semantics of the generated trajectory at both the point and trajectory levels. Finally, we employ a Destination-Oriented Navigator to seamlessly integrate destination-oriented guidance. Extensive experiments on three real-world datasets demonstrate that HOSER outperforms state-of-the-art baselines by a significant margin. Moreover, the model's performance in few-shot learning and zero-shot learning scenarios further verifies the effectiveness of our holistic semantic representation.

Recent techniques for text-to-4D generation synthesize dynamic 3D scenes using supervision from pre-trained text-to-video models. However, existing representations for motion, such as deformation models or time-dependent neural representations, are limited in the amount of motion they can generate-they cannot synthesize motion extending far beyond the bounding box used for volume rendering. The lack of a more flexible motion model contributes to the gap in realism between 4D generation methods and recent, near-photorealistic video generation models. Here, we propose TC4D: trajectory-conditioned text-to-4D generation, which factors motion into global and local components. We represent the global motion of a scene's bounding box using rigid transformation along a trajectory parameterized by a spline. We learn local deformations that conform to the global trajectory using supervision from a text-to-video model. Our approach enables the synthesis of scenes animated along arbitrary trajectories, compositional scene generation, and significant improvements to the realism and amount of generated motion, which we evaluate qualitatively and through a user study. Video results can be viewed on our website: https://sherwinbahmani.github.io/tc4d.

We present TrajectoryCrafter, a novel approach to redirect camera trajectories for monocular videos. By disentangling deterministic view transformations from stochastic content generation, our method achieves precise control over user-specified camera trajectories. We propose a novel dual-stream conditional video diffusion model that concurrently integrates point cloud renders and source videos as conditions, ensuring accurate view transformations and coherent 4D content generation. Instead of leveraging scarce multi-view videos, we curate a hybrid training dataset combining web-scale monocular videos with static multi-view datasets, by our innovative double-reprojection strategy, significantly fostering robust generalization across diverse scenes. Extensive evaluations on multi-view and large-scale monocular videos demonstrate the superior performance of our method.

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.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.

Computer use agents (CUAs) need to plan task workflows grounded in diverse, ever-changing applications and environments, but learning is hindered by the scarcity of large-scale, high-quality training data in the target application. Existing datasets are domain-specific, static, and costly to annotate, while current synthetic data generation methods often yield simplistic or misaligned task demonstrations. To address these limitations, we introduce Watch & Learn (W&L), a framework that converts human demonstration videos readily available on the Internet into executable UI trajectories at scale. Instead of directly generating trajectories or relying on ad hoc reasoning heuristics, we cast the problem as an inverse dynamics objective: predicting the user's action from consecutive screen states. This formulation reduces manual engineering, is easier to learn, and generalizes more robustly across applications. Concretely, we develop an inverse dynamics labeling pipeline with task-aware video retrieval, generate over 53k high-quality trajectories from raw web videos, and demonstrate that these trajectories improve CUAs both as in-context demonstrations and as supervised training data. On the challenging OSWorld benchmark, UI trajectories extracted with W&L consistently enhance both general-purpose and state-of-the-art frameworks in-context, and deliver stronger gains for open-source models under supervised training. These results highlight web-scale human demonstration videos as a practical and scalable foundation for advancing CUAs towards real-world deployment.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

Modern continuous-time generative models typically induce V-shaped flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the hierarchical structures that exist in real-world data. To address this, we introduce Y-shaped generative flows, a framework in which samples travel together along shared pathways before branching off to target-specific endpoints. Our formulation is theoretically justified, yet remains practical, requiring only minimal modifications to standard velocity-driven models. We implement this through a scalable, neural network-based training objective. Experiments on synthetic, image, and biological datasets demonstrate that our method recovers hierarchy-aware structures, improves distributional metrics over strong flow-based baselines, and reaches targets in fewer steps.

We propose a new problem, In-2-4D, for generative 4D (i.e., 3D + motion) inbetweening from a minimalistic input setting: two single-view images capturing an object in two distinct motion states. Given two images representing the start and end states of an object in motion, our goal is to generate and reconstruct the motion in 4D. We utilize a video interpolation model to predict the motion, but large frame-to-frame motions can lead to ambiguous interpretations. To overcome this, we employ a hierarchical approach to identify keyframes that are visually close to the input states and show significant motion, then generate smooth fragments between them. For each fragment, we construct the 3D representation of the keyframe using Gaussian Splatting. The temporal frames within the fragment guide the motion, enabling their transformation into dynamic Gaussians through a deformation field. To improve temporal consistency and refine 3D motion, we expand the self-attention of multi-view diffusion across timesteps and apply rigid transformation regularization. Finally, we merge the independently generated 3D motion segments by interpolating boundary deformation fields and optimizing them to align with the guiding video, ensuring smooth and flicker-free transitions. Through extensive qualitative and quantitiave experiments as well as a user study, we show the effectiveness of our method and its components. The project page is available at https://in-2-4d.github.io/

We introduce a method for generating realistic pedestrian trajectories and full-body animations that can be controlled to meet user-defined goals. We draw on recent advances in guided diffusion modeling to achieve test-time controllability of trajectories, which is normally only associated with rule-based systems. Our guided diffusion model allows users to constrain trajectories through target waypoints, speed, and specified social groups while accounting for the surrounding environment context. This trajectory diffusion model is integrated with a novel physics-based humanoid controller to form a closed-loop, full-body pedestrian animation system capable of placing large crowds in a simulated environment with varying terrains. We further propose utilizing the value function learned during RL training of the animation controller to guide diffusion to produce trajectories better suited for particular scenarios such as collision avoidance and traversing uneven terrain. Video results are available on the project page at https://nv-tlabs.github.io/trace-pace .

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

Agentic applications based on large language models increasingly rely on multi-step interaction loops involving planning, action execution, and environment feedback. While such systems are now deployed at scale, improving them post-deployment remains challenging. Agent trajectories are voluminous and non-deterministic, and reviewing each one, whether through human review or auxiliary LLMs, is slow and cost-prohibitive. We propose a lightweight, signal-based framework for triaging agentic interaction trajectories. Our approach computes cheap, broadly applicable signals from live interactions and attaches them as structured attributes for trajectory triage, identifying interactions likely to be informative without affecting online agent behavior. We organize signals into a coarse-grained taxonomy spanning interaction (misalignment, stagnation, disengagement, satisfaction), execution (failure, loop), and environment (exhaustion), designed for computation without model calls. In a controlled annotation study on τ-bench, a widely used benchmark for tool-augmented agent evaluation, we show that signal-based sampling achieves an 82\% informativeness rate compared to 74\% for heuristic filtering and 54\% for random sampling, with a 1.52x efficiency gain per informative trajectory. The advantage is robust across reward strata and task domains, confirming that signals provide genuine per-trajectory informativeness gains rather than merely oversampling obvious failures. These results show that lightweight signals can serve as practical sampling infrastructure for agentic systems, and suggest a path toward preference data construction and post-deployment optimization.

Imitation learning method has shown immense promise for robotic manipulation, yet its practical deployment is fundamentally constrained by the data scarcity. Despite prior work on collecting large-scale datasets, there still remains a significant gap to robust spatial generalization. We identify a key limitation: individual trajectories, regardless of their length, are typically collected from a single, static spatial configuration of the environment. This includes fixed object and target spatial positions as well as unchanging camera viewpoints, which significantly restricts the diversity of spatial information available for learning. To address this critical bottleneck in data efficiency, we propose MOtion-Based Variability Enhancement (MOVE), a simple yet effective data collection paradigm that enables the acquisition of richer spatial information from dynamic demonstrations. Our core contribution is an augmentation strategy that injects motion into any movable objects within the environment for each demonstration. This process implicitly generates a dense and diverse set of spatial configurations within a single trajectory. We conduct extensive experiments in both simulation and real-world environments to validate our approach. For example, in simulation tasks requiring strong spatial generalization, MOVE achieves an average success rate of 39.1\%, a 76.1\% relative improvement over the static data collection paradigm (22.2\%), and yields up to 2--5times gains in data efficiency on certain tasks. Our code is available at https://github.com/lucywang720/MOVE.

Accumulating substantial volumes of real-world driving data proves pivotal in the realm of trajectory forecasting for autonomous driving. Given the heavy reliance of current trajectory forecasting models on data-driven methodologies, we aim to tackle the challenge of learning general trajectory forecasting representations under limited data availability. We propose a pipeline-level solution to mitigate the issue of data scarcity in trajectory forecasting. The solution is composed of two parts: firstly, we adopt HD map augmentation and trajectory synthesis for generating driving data, and then we learn representations by pre-training on them. Specifically, we apply vector transformations to reshape the maps, and then employ a rule-based model to generate trajectories on both original and augmented scenes; thus enlarging the driving data without collecting additional real ones. To foster the learning of general representations within this augmented dataset, we comprehensively explore the different pre-training strategies, including extending the concept of a Masked AutoEncoder (MAE) for trajectory forecasting. Without bells and whistles, our proposed pipeline-level solution is general, simple, yet effective: we conduct extensive experiments to demonstrate the effectiveness of our data expansion and pre-training strategies, which outperform the baseline prediction model by large margins, e.g. 5.04%, 3.84% and 8.30% in terms of MR_6, minADE_6 and minFDE_6. The pre-training dataset and the codes for pre-training and fine-tuning are released at https://github.com/yhli123/Pretraining_on_Synthetic_Driving_Data_for_Trajectory_Prediction.

We propose GoalFlow, an end-to-end autonomous driving method for generating high-quality multimodal trajectories. In autonomous driving scenarios, there is rarely a single suitable trajectory. Recent methods have increasingly focused on modeling multimodal trajectory distributions. However, they suffer from trajectory selection complexity and reduced trajectory quality due to high trajectory divergence and inconsistencies between guidance and scene information. To address these issues, we introduce GoalFlow, a novel method that effectively constrains the generative process to produce high-quality, multimodal trajectories. To resolve the trajectory divergence problem inherent in diffusion-based methods, GoalFlow constrains the generated trajectories by introducing a goal point. GoalFlow establishes a novel scoring mechanism that selects the most appropriate goal point from the candidate points based on scene information. Furthermore, GoalFlow employs an efficient generative method, Flow Matching, to generate multimodal trajectories, and incorporates a refined scoring mechanism to select the optimal trajectory from the candidates. Our experimental results, validated on the NavsimDauner2024_navsim, demonstrate that GoalFlow achieves state-of-the-art performance, delivering robust multimodal trajectories for autonomous driving. GoalFlow achieved PDMS of 90.3, significantly surpassing other methods. Compared with other diffusion-policy-based methods, our approach requires only a single denoising step to obtain excellent performance. The code is available at https://github.com/YvanYin/GoalFlow.

The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple solutions for motion planning, they are limited to generating a finite set of solutions. To address this issue, we presents an optimization method that learns an infinite set of solutions in trajectory optimization. In our framework, diverse solutions are obtained by learning latent representations of solutions. Our approach can be interpreted as training a deep generative model of collision-free trajectories for motion planning. The experimental results indicate that the trained model represents an infinite set of homotopic solutions for motion planning problems.

Trajectory data, capturing human actions and environmental states across various modalities, holds significant potential for enhancing AI agent capabilities, particularly in GUI environments. However, how to model the representation of trajectory-level data presents a significant challenge that has not been systematically addressed amid explosive trajectory data growth. In this work, we introduce Multimodal Trajectory Retrieval, bridging the gap between universal retrieval and agent-centric trajectory modeling. We construct the Unified Agent Trajectory Dataset (UATD) from annotated demonstrations and states across diverse real-world scenarios. Based on this, we present GAE-Bench, a benchmark containing a large number of trajectory-based retrieval pairs. In addition, we propose GAE-Retriever, a multimodal retrieval framework that adopts vision-language models and incorporates optimized contrastive learning through a token selection and the GradCache mechanism. Comprehensive evaluations across multiple datasets show that GAE-Retriever consistently outperforms strong baselines in retrieval recall, highlighting its effectiveness in advancing multimodal trajectory retrieval.

Effective self-supervised learning (SSL) techniques have been key to unlocking large datasets for representation learning. While many promising methods have been developed using online corpora and captioned photographs, their application to scientific domains, where data encodes highly specialized knowledge, remains a challenge. Liquid Argon Time Projection Chambers (LArTPCs) provide high-resolution 3D imaging for fundamental physics, but analysis of their sparse, complex point cloud data often relies on supervised methods trained on large simulations, introducing potential biases. We introduce the Point-based Liquid Argon Masked Autoencoder (PoLAr-MAE), applying masked point modeling to unlabeled LArTPC images using domain-specific volumetric tokenization and energy prediction. We show this SSL approach learns physically meaningful trajectory representations directly from data. This yields remarkable data efficiency: fine-tuning on just 100 labeled events achieves track/shower semantic segmentation performance comparable to the state-of-the-art supervised baseline trained on >100,000 events. Furthermore, internal attention maps exhibit emergent instance segmentation of particle trajectories. While challenges remain, particularly for fine-grained features, we make concrete SSL's potential for building a foundation model for LArTPC image analysis capable of serving as a common base for all data reconstruction tasks. To facilitate further progress, we release PILArNet-M, a large dataset of 1M LArTPC events. Project site: https://youngsm.com/polarmae.

We introduce EMMA, an End-to-end Multimodal Model for Autonomous driving. Built on a multi-modal large language model foundation, EMMA directly maps raw camera sensor data into various driving-specific outputs, including planner trajectories, perception objects, and road graph elements. EMMA maximizes the utility of world knowledge from the pre-trained large language models, by representing all non-sensor inputs (e.g. navigation instructions and ego vehicle status) and outputs (e.g. trajectories and 3D locations) as natural language text. This approach allows EMMA to jointly process various driving tasks in a unified language space, and generate the outputs for each task using task-specific prompts. Empirically, we demonstrate EMMA's effectiveness by achieving state-of-the-art performance in motion planning on nuScenes as well as competitive results on the Waymo Open Motion Dataset (WOMD). EMMA also yields competitive results for camera-primary 3D object detection on the Waymo Open Dataset (WOD). We show that co-training EMMA with planner trajectories, object detection, and road graph tasks yields improvements across all three domains, highlighting EMMA's potential as a generalist model for autonomous driving applications. However, EMMA also exhibits certain limitations: it can process only a small amount of image frames, does not incorporate accurate 3D sensing modalities like LiDAR or radar and is computationally expensive. We hope that our results will inspire further research to mitigate these issues and to further evolve the state of the art in autonomous driving model architectures.

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

Generative models have gained significant traction in offline reinforcement learning (RL) due to their ability to model complex trajectory distributions. However, existing generation-based approaches still struggle with long-horizon tasks characterized by sparse rewards. Some hierarchical generation methods have been developed to mitigate this issue by decomposing the original problem into shorter-horizon subproblems using one policy and generating detailed actions with another. While effective, these methods often overlook the multi-scale temporal structure inherent in trajectories, resulting in suboptimal performance. To overcome these limitations, we propose MAGE, a Multi-scale Autoregressive GEneration-based offline RL method. MAGE incorporates a condition-guided multi-scale autoencoder to learn hierarchical trajectory representations, along with a multi-scale transformer that autoregressively generates trajectory representations from coarse to fine temporal scales. MAGE effectively captures temporal dependencies of trajectories at multiple resolutions. Additionally, a condition-guided decoder is employed to exert precise control over short-term behaviors. Extensive experiments on five offline RL benchmarks against fifteen baseline algorithms show that MAGE successfully integrates multi-scale trajectory modeling with conditional guidance, generating coherent and controllable trajectories in long-horizon sparse-reward settings.

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple, this combination has a number of empirical shortcomings, suggesting that learned models may not be well-suited to standard trajectory optimization. In this paper, we consider what it would look like to fold as much of the trajectory optimization pipeline as possible into the modeling problem, such that sampling from the model and planning with it become nearly identical. The core of our technical approach lies in a diffusion probabilistic model that plans by iteratively denoising trajectories. We show how classifier-guided sampling and image inpainting can be reinterpreted as coherent planning strategies, explore the unusual and useful properties of diffusion-based planning methods, and demonstrate the effectiveness of our framework in control settings that emphasize long-horizon decision-making and test-time flexibility.

We present a novel approach for traffic forecasting in urban traffic scenarios using a combination of spectral graph analysis and deep learning. We predict both the low-level information (future trajectories) as well as the high-level information (road-agent behavior) from the extracted trajectory of each road-agent. Our formulation represents the proximity between the road agents using a weighted dynamic geometric graph (DGG). We use a two-stream graph-LSTM network to perform traffic forecasting using these weighted DGGs. The first stream predicts the spatial coordinates of road-agents, while the second stream predicts whether a road-agent is going to exhibit overspeeding, underspeeding, or neutral behavior by modeling spatial interactions between road-agents. Additionally, we propose a new regularization algorithm based on spectral clustering to reduce the error margin in long-term prediction (3-5 seconds) and improve the accuracy of the predicted trajectories. Moreover, we prove a theoretical upper bound on the regularized prediction error. We evaluate our approach on the Argoverse, Lyft, Apolloscape, and NGSIM datasets and highlight the benefits over prior trajectory prediction methods. In practice, our approach reduces the average prediction error by approximately 75% over prior algorithms and achieves a weighted average accuracy of 91.2% for behavior prediction. Additionally, our spectral regularization improves long-term prediction by up to 70%.

We focus on the utilisation of reactive trajectory imitation controllers for goal-directed mobile robot navigation. We propose a topological navigation graph (TNG) - an imitation-learning-based framework for navigating through environments with intersecting trajectories. The TNG framework represents the environment as a directed graph composed of deep neural networks. Each vertex of the graph corresponds to a trajectory and is represented by a trajectory identification classifier and a trajectory imitation controller. For trajectory following, we propose the novel use of neural object detection architectures. The edges of TNG correspond to intersections between trajectories and are all represented by a classifier. We provide empirical evaluation of the proposed navigation framework and its components in simulated and real-world environments, demonstrating that TNG allows us to utilise non-goal-directed, imitation-learning methods for goal-directed autonomous navigation.

The recent advancement of autonomous agents powered by Large Language Models (LLMs) has demonstrated significant potential for automating tasks on mobile devices through graphical user interfaces (GUIs). Despite initial progress, these agents still face challenges when handling complex real-world tasks. These challenges arise from a lack of knowledge about real-life mobile applications in LLM-based agents, which may lead to ineffective task planning and even cause hallucinations. To address these challenges, we propose a novel LLM-based agent framework called MapAgent that leverages memory constructed from historical trajectories to augment current task planning. Specifically, we first propose a trajectory-based memory mechanism that transforms task execution trajectories into a reusable and structured page-memory database. Each page within a trajectory is extracted as a compact yet comprehensive snapshot, capturing both its UI layout and functional context. Secondly, we introduce a coarse-to-fine task planning approach that retrieves relevant pages from the memory database based on similarity and injects them into the LLM planner to compensate for potential deficiencies in understanding real-world app scenarios, thereby achieving more informed and context-aware task planning. Finally, planned tasks are transformed into executable actions through a task executor supported by a dual-LLM architecture, ensuring effective tracking of task progress. Experimental results in real-world scenarios demonstrate that MapAgent achieves superior performance to existing methods. The code will be open-sourced to support further research.

Trajectory-Guided image-to-video (I2V) generation aims to synthesize videos that adhere to user-specified motion instructions. Existing methods typically rely on computationally expensive fine-tuning on scarce annotated datasets. Although some zero-shot methods attempt to trajectory control in the latent space, they may yield unrealistic motion by neglecting 3D perspective and creating a misalignment between the manipulated latents and the network's noise predictions. To address these challenges, we introduce Zo3T, a novel zero-shot test-time-training framework for trajectory-guided generation with three core innovations: First, we incorporate a 3D-Aware Kinematic Projection, leveraging inferring scene depth to derive perspective-correct affine transformations for target regions. Second, we introduce Trajectory-Guided Test-Time LoRA, a mechanism that dynamically injects and optimizes ephemeral LoRA adapters into the denoising network alongside the latent state. Driven by a regional feature consistency loss, this co-adaptation effectively enforces motion constraints while allowing the pre-trained model to locally adapt its internal representations to the manipulated latent, thereby ensuring generative fidelity and on-manifold adherence. Finally, we develop Guidance Field Rectification, which refines the denoising evolutionary path by optimizing the conditional guidance field through a one-step lookahead strategy, ensuring efficient generative progression towards the target trajectory. Zo3T significantly enhances 3D realism and motion accuracy in trajectory-controlled I2V generation, demonstrating superior performance over existing training-based and zero-shot approaches.

We present Lang2Motion, a framework for language-guided point trajectory generation by aligning motion manifolds with joint embedding spaces. Unlike prior work focusing on human motion or video synthesis, we generate explicit trajectories for arbitrary objects using motion extracted from real-world videos via point tracking. Our transformer-based auto-encoder learns trajectory representations through dual supervision: textual motion descriptions and rendered trajectory visualizations, both mapped through CLIP's frozen encoders. Lang2Motion achieves 34.2% Recall@1 on text-to-trajectory retrieval, outperforming video-based methods by 12.5 points, and improves motion accuracy by 33-52% (12.4 ADE vs 18.3-25.3) compared to video generation baselines. We demonstrate 88.3% Top-1 accuracy on human action recognition despite training only on diverse object motions, showing effective transfer across motion domains. Lang2Motion supports style transfer, semantic interpolation, and latent-space editing through CLIP-aligned trajectory representations.

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

Classification of movement trajectories has many applications in transportation. Supervised neural models represent the current state-of-the-art. Recent security applications require this task to be rapidly employed in environments that may differ from the data used to train such models for which there is little training data. We provide a neuro-symbolic rule-based framework to conduct error correction and detection of these models to support eventual deployment in security applications. We provide a suite of experiments on several recent and state-of-the-art models and show an accuracy improvement of 1.7% over the SOTA model in the case where all classes are present in training and when 40% of classes are omitted from training, we obtain a 5.2% improvement (zero-shot) and 23.9% (few-shot) improvement over the SOTA model without resorting to retraining of the base model.

In the recent years, the rapid spread of mobile device has create the vast amount of mobile data. However, some shallow-structure models such as support vector machine (SVM) have difficulty dealing with high dimensional data with the development of mobile network. In this paper, we analyze mobile data to predict human trajectories in order to understand human mobility pattern via a deep-structure model called "DeepSpace". To the best of out knowledge, it is the first time that the deep learning approach is applied to predicting human trajectories. Furthermore, we develop the vanilla convolutional neural network (CNN) to be an online learning system, which can deal with the continuous mobile data stream. In general, "DeepSpace" consists of two different prediction models corresponding to different scales in space (the coarse prediction model and fine prediction models). This two models constitute a hierarchical structure, which enable the whole architecture to be run in parallel. Finally, we test our model based on the data usage detail records (UDRs) from the mobile cellular network in a city of southeastern China, instead of the call detail records (CDRs) which are widely used by others as usual. The experiment results show that "DeepSpace" is promising in human trajectories prediction.

We propose a novel algorithm for accelerating dense long-term 3D point tracking in videos. Through analysis of existing state-of-the-art methods, we identify two major computational bottlenecks. First, transformer-based iterative tracking becomes expensive when handling a large number of trajectories. To address this, we introduce a coarse-to-fine strategy that begins tracking with a small subset of points and progressively expands the set of tracked trajectories. The newly added trajectories are initialized using a learnable interpolation module, which is trained end-to-end alongside the tracking network. Second, we propose an optimization that significantly reduces the cost of correlation feature computation, another key bottleneck in prior methods. Together, these improvements lead to a 5-100x speedup over existing approaches while maintaining state-of-the-art tracking accuracy.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

We consider the problem of segmenting objects in videos based on their motion and no other forms of supervision. Prior work has often approached this problem by using the principle of common fate, namely the fact that the motion of points that belong to the same object is strongly correlated. However, most authors have only considered instantaneous motion from optical flow. In this work, we present a way to train a segmentation network using long-term point trajectories as a supervisory signal to complement optical flow. The key difficulty is that long-term motion, unlike instantaneous motion, is difficult to model -- any parametric approximation is unlikely to capture complex motion patterns over long periods of time. We instead draw inspiration from subspace clustering approaches, proposing a loss function that seeks to group the trajectories into low-rank matrices where the motion of object points can be approximately explained as a linear combination of other point tracks. Our method outperforms the prior art on motion-based segmentation, which shows the utility of long-term motion and the effectiveness of our formulation.

Temporal motion modeling has always been a key component in multiple object tracking (MOT) which can ensure smooth trajectory movement and provide accurate positional information to enhance association precision. However, current motion models struggle to be both efficient and effective across different application scenarios. To this end, we propose TrackSSM inspired by the recently popular state space models (SSM), a unified encoder-decoder motion framework that uses data-dependent state space model to perform temporal motion of trajectories. Specifically, we propose Flow-SSM, a module that utilizes the position and motion information from historical trajectories to guide the temporal state transition of object bounding boxes. Based on Flow-SSM, we design a flow decoder. It is composed of a cascaded motion decoding module employing Flow-SSM, which can use the encoded flow information to complete the temporal position prediction of trajectories. Additionally, we propose a Step-by-Step Linear (S^2L) training strategy. By performing linear interpolation between the positions of the object in the previous frame and the current frame, we construct the pseudo labels of step-by-step linear training, ensuring that the trajectory flow information can better guide the object bounding box in completing temporal transitions. TrackSSM utilizes a simple Mamba-Block to build a motion encoder for historical trajectories, forming a temporal motion model with an encoder-decoder structure in conjunction with the flow decoder. TrackSSM is applicable to various tracking scenarios and achieves excellent tracking performance across multiple benchmarks, further extending the potential of SSM-like temporal motion models in multi-object tracking tasks. Code and models are publicly available at https://github.com/Xavier-Lin/TrackSSM.

Path-velocity decomposition is an intuitive yet powerful approach to address the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler, steps: first, find a path in the configuration space that satisfies the geometric constraints (path planning), and second, find a time-parameterization of that path satisfying the kinodynamic constraints. A fundamental requirement is that the path found in the first step should be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints in the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm -- Admissible Velocity Propagation -- which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path while respecting the system kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.

Video diffusion models (VDMs) have advanced significantly in recent years, enabling the generation of highly realistic videos and drawing the attention of the community in their potential as world simulators. However, despite their capabilities, VDMs often fail to produce physically plausible videos due to an inherent lack of understanding of physics, resulting in incorrect dynamics and event sequences. To address this limitation, we propose a novel two-stage image-to-video generation framework that explicitly incorporates physics. In the first stage, we employ a Vision Language Model (VLM) as a coarse-grained motion planner, integrating chain-of-thought and physics-aware reasoning to predict a rough motion trajectories/changes that approximate real-world physical dynamics while ensuring the inter-frame consistency. In the second stage, we use the predicted motion trajectories/changes to guide the video generation of a VDM. As the predicted motion trajectories/changes are rough, noise is added during inference to provide freedom to the VDM in generating motion with more fine details. Extensive experimental results demonstrate that our framework can produce physically plausible motion, and comparative evaluations highlight the notable superiority of our approach over existing methods. More video results are available on our Project Page: https://madaoer.github.io/projects/physically_plausible_video_generation.

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

Next POI recommendation intends to forecast users' immediate future movements given their current status and historical information, yielding great values for both users and service providers. However, this problem is perceptibly complex because various data trends need to be considered together. This includes the spatial locations, temporal contexts, user's preferences, etc. Most existing studies view the next POI recommendation as a sequence prediction problem while omitting the collaborative signals from other users. Instead, we propose a user-agnostic global trajectory flow map and a novel Graph Enhanced Transformer model (GETNext) to better exploit the extensive collaborative signals for a more accurate next POI prediction, and alleviate the cold start problem in the meantime. GETNext incorporates the global transition patterns, user's general preference, spatio-temporal context, and time-aware category embeddings together into a transformer model to make the prediction of user's future moves. With this design, our model outperforms the state-of-the-art methods with a large margin and also sheds light on the cold start challenges within the spatio-temporal involved recommendation problems.

Video generation models have shown strong potential as world models for autonomous driving simulation. However, existing approaches are primarily trained on real-world driving datasets, which mostly contain natural and safe driving scenarios. As a result, current models often fail when conditioned on challenging or counterfactual trajectories-such as imperfect trajectories generated by simulators or planning systems-producing videos with severe physical inconsistencies and artifacts. To address this limitation, we propose PhyGenesis, a world model designed to generate driving videos with high visual fidelity and strong physical consistency. Our framework consists of two key components: (1) a physical condition generator that transforms potentially invalid trajectory inputs into physically plausible conditions, and (2) a physics-enhanced video generator that produces high-fidelity multi-view driving videos under these conditions. To effectively train these components, we construct a large-scale, physics-rich heterogeneous dataset. Specifically, in addition to real-world driving videos, we generate diverse challenging driving scenarios using the CARLA simulator, from which we derive supervision signals that guide the model to learn physically grounded dynamics under extreme conditions. This challenging-trajectory learning strategy enables trajectory correction and promotes physically consistent video generation. Extensive experiments demonstrate that PhyGenesis consistently outperforms state-of-the-art methods, especially on challenging trajectories. Our project page is available at: https://wm-research.github.io/PhyGenesis/.

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

Next Location Prediction is a fundamental task in the study of human mobility, with wide-ranging applications in transportation planning, urban governance, and epidemic forecasting. In practice, when humans attempt to predict the next location in a trajectory, they often visualize the trajectory on a map and reason based on road connectivity and movement trends. However, the vast majority of existing next-location prediction models do not reason over maps in the way that humans do. Fortunately, the recent development of Vision-Language Models (VLMs) has demonstrated strong capabilities in visual perception and even visual reasoning. This opens up a new possibility: by rendering both the road network and trajectory onto an image and leveraging the reasoning abilities of VLMs, we can enable models to perform trajectory inference in a human-like manner. To explore this idea, we first propose a method called Vision-Guided Location Search (VGLS), which evaluates whether a general-purpose VLM is capable of trajectory-based reasoning without modifying any of its internal parameters. Based on insights from the VGLS results, we further propose our main approach: VLMLocPredictor, which is composed of two stages: In the first stage, we design two Supervised Fine-Tuning (SFT) tasks that help the VLM understand road network and trajectory structures and acquire basic reasoning ability on such visual inputs. In the second stage, we introduce Reinforcement Learning from Visual Map Feedback, enabling the model to self-improve its next-location prediction ability through interaction with the environment. Experiments conducted on datasets from four different cities show that our method achieves state-of-the-art (SOTA) performance and exhibits superior cross-city generalization compared to other LLM-based approaches.

Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

Advances in video generation have significantly improved the realism and quality of created scenes. This has fueled interest in developing intuitive tools that let users leverage video generation as world simulators. Text-to-video (T2V) generation is one such approach, enabling video creation from text descriptions only. Yet, due to the inherent ambiguity in texts and the limited temporal information offered by text prompts, researchers have explored additional control signals like trajectory-guided systems, for more accurate T2V generation. Nonetheless, methods to evaluate whether T2V models can generate realistic interactions between multiple objects are lacking. We introduce InTraGen, a pipeline for improved trajectory-based generation of object interaction scenarios. We propose 4 new datasets and a novel trajectory quality metric to evaluate the performance of the proposed InTraGen. To achieve object interaction, we introduce a multi-modal interaction encoding pipeline with an object ID injection mechanism that enriches object-environment interactions. Our results demonstrate improvements in both visual fidelity and quantitative performance. Code and datasets are available at https://github.com/insait-institute/InTraGen

When studying unconstrained behaviour and allowing mice to leave their cage to navigate a complex labyrinth, the mice exhibit foraging behaviour in the labyrinth searching for rewards, returning to their home cage now and then, e.g. to drink. Surprisingly, when executing such a ``home run'', the mice do not follow the exact reverse path, in fact, the entry path and home path have very little overlap. Recent work proposed a hierarchical active inference model for navigation, where the low level model makes inferences about hidden states and poses that explain sensory inputs, whereas the high level model makes inferences about moving between locations, effectively building a map of the environment. However, using this ``map'' for planning, only allows the agent to find trajectories that it previously explored, far from the observed mice's behaviour. In this paper, we explore ways of incorporating before-unvisited paths in the planning algorithm, by using the low level generative model to imagine potential, yet undiscovered paths. We demonstrate a proof of concept in a grid-world environment, showing how an agent can accurately predict a new, shorter path in the map leading to its starting point, using a generative model learnt from pixel-based observations.

Recent video generation approaches increasingly rely on planning intermediate control signals such as object trajectories to improve temporal coherence and motion fidelity. However, these methods mostly employ single-shot plans that are typically limited to simple motions, or iterative refinement which requires multiple calls to the video generator, incuring high computational cost. To overcome these limitations, we propose SketchVerify, a training-free, sketch-verification-based planning framework that improves motion planning quality with more dynamically coherent trajectories (i.e., physically plausible and instruction-consistent motions) prior to full video generation by introducing a test-time sampling and verification loop. Given a prompt and a reference image, our method predicts multiple candidate motion plans and ranks them using a vision-language verifier that jointly evaluates semantic alignment with the instruction and physical plausibility. To efficiently score candidate motion plans, we render each trajectory as a lightweight video sketch by compositing objects over a static background, which bypasses the need for expensive, repeated diffusion-based synthesis while achieving comparable performance. We iteratively refine the motion plan until a satisfactory one is identified, which is then passed to the trajectory-conditioned generator for final synthesis. Experiments on WorldModelBench and PhyWorldBench demonstrate that our method significantly improves motion quality, physical realism, and long-term consistency compared to competitive baselines while being substantially more efficient. Our ablation study further shows that scaling up the number of trajectory candidates consistently enhances overall performance.

Tracking pixels in videos is typically studied as an optical flow estimation problem, where every pixel is described with a displacement vector that locates it in the next frame. Even though wider temporal context is freely available, prior efforts to take this into account have yielded only small gains over 2-frame methods. In this paper, we revisit Sand and Teller's "particle video" approach, and study pixel tracking as a long-range motion estimation problem, where every pixel is described with a trajectory that locates it in multiple future frames. We re-build this classic approach using components that drive the current state-of-the-art in flow and object tracking, such as dense cost maps, iterative optimization, and learned appearance updates. We train our models using long-range amodal point trajectories mined from existing optical flow data that we synthetically augment with multi-frame occlusions. We test our approach in trajectory estimation benchmarks and in keypoint label propagation tasks, and compare favorably against state-of-the-art optical flow and feature tracking methods.

Micro Aerial Vehicles (MAVs) that operate in unstructured, unexplored environments require fast and flexible local planning, which can replan when new parts of the map are explored. Trajectory optimization methods fulfill these needs, but require obstacle distance information, which can be given by Euclidean Signed Distance Fields (ESDFs). We propose a method to incrementally build ESDFs from Truncated Signed Distance Fields (TSDFs), a common implicit surface representation used in computer graphics and vision. TSDFs are fast to build and smooth out sensor noise over many observations, and are designed to produce surface meshes. Meshes allow human operators to get a better assessment of the robot's environment, and set high-level mission goals. We show that we can build TSDFs faster than Octomaps, and that it is more accurate to build ESDFs out of TSDFs than occupancy maps. Our complete system, called voxblox, will be available as open source and runs in real-time on a single CPU core. We validate our approach on-board an MAV, by using our system with a trajectory optimization local planner, entirely on-board and in real-time.

This paper addresses the long-standing challenge of reconstructing 3D structures from videos with dynamic content. Current approaches to this problem were not designed to operate on casual videos recorded by standard cameras or require a long optimization time. Aiming to significantly improve the efficiency of previous approaches, we present TracksTo4D, a learning-based approach that enables inferring 3D structure and camera positions from dynamic content originating from casual videos using a single efficient feed-forward pass. To achieve this, we propose operating directly over 2D point tracks as input and designing an architecture tailored for processing 2D point tracks. Our proposed architecture is designed with two key principles in mind: (1) it takes into account the inherent symmetries present in the input point tracks data, and (2) it assumes that the movement patterns can be effectively represented using a low-rank approximation. TracksTo4D is trained in an unsupervised way on a dataset of casual videos utilizing only the 2D point tracks extracted from the videos, without any 3D supervision. Our experiments show that TracksTo4D can reconstruct a temporal point cloud and camera positions of the underlying video with accuracy comparable to state-of-the-art methods, while drastically reducing runtime by up to 95\%. We further show that TracksTo4D generalizes well to unseen videos of unseen semantic categories at inference time.

We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at https://youtu.be/SWbofjhyPzI

Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, Stable Sparse-RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.