Daily Papers

Monocular depth estimation is crucial for numerous downstream vision tasks and applications. Current discriminative approaches to this problem are limited due to blurry artifacts, while state-of-the-art generative methods suffer from slow sampling due to their SDE nature. Rather than starting from noise, we seek a direct mapping from input image to depth map. We observe that this can be effectively framed using flow matching, since its straight trajectories through solution space offer efficiency and high quality. Our study demonstrates that a pre-trained image diffusion model can serve as an adequate prior for a flow matching depth model, allowing efficient training on only synthetic data to generalize to real images. We find that an auxiliary surface normals loss further improves the depth estimates. Due to the generative nature of our approach, our model reliably predicts the confidence of its depth estimates. On standard benchmarks of complex natural scenes, our lightweight approach exhibits state-of-the-art performance at favorable low computational cost despite only being trained on little synthetic data.

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at https://github.com/mlvlab/CAF{https://github.com/mlvlab/CAF}.

Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows, which iteratively learn smooth ODE paths that are less susceptible to truncation error. However, rectified flows still require a relatively large number of function evaluations (NFEs). In this work, we propose improved techniques for training rectified flows, allowing them to compete with knowledge distillation methods even in the low NFE setting. Our main insight is that under realistic settings, a single iteration of the Reflow algorithm for training rectified flows is sufficient to learn nearly straight trajectories; hence, the current practice of using multiple Reflow iterations is unnecessary. We thus propose techniques to improve one-round training of rectified flows, including a U-shaped timestep distribution and LPIPS-Huber premetric. With these techniques, we improve the FID of the previous 2-rectified flow by up to 72% in the 1 NFE setting on CIFAR-10. On ImageNet 64times64, our improved rectified flow outperforms the state-of-the-art distillation methods such as consistency distillation and progressive distillation in both one-step and two-step settings and rivals the performance of improved consistency training (iCT) in FID. Code is available at https://github.com/sangyun884/rfpp.

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the fixed linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories. This exploration underscores NFDM's versatility and its potential for a wide range of applications.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Existing video frame interpolation (VFI) methods blindly predict where each object is at a specific timestep t ("time indexing"), which struggles to predict precise object movements. Given two images of a baseball, there are infinitely many possible trajectories: accelerating or decelerating, straight or curved. This often results in blurry frames as the method averages out these possibilities. Instead of forcing the network to learn this complicated time-to-location mapping implicitly together with predicting the frames, we provide the network with an explicit hint on how far the object has traveled between start and end frames, a novel approach termed "distance indexing". This method offers a clearer learning goal for models, reducing the uncertainty tied to object speeds. We further observed that, even with this extra guidance, objects can still be blurry especially when they are equally far from both input frames (i.e., halfway in-between), due to the directional ambiguity in long-range motion. To solve this, we propose an iterative reference-based estimation strategy that breaks down a long-range prediction into several short-range steps. When integrating our plug-and-play strategies into state-of-the-art learning-based models, they exhibit markedly sharper outputs and superior perceptual quality in arbitrary time interpolations, using a uniform distance indexing map in the same format as time indexing. Additionally, distance indexing can be specified pixel-wise, which enables temporal manipulation of each object independently, offering a novel tool for video editing tasks like re-timing.

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

We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to generative modeling and domain transfer, among various other tasks involving distribution transport. The idea of rectified flow is to learn the ODE to follow the straight paths connecting the points drawn from \pi_0 and \pi_1 as much as possible. This is achieved by solving a straightforward nonlinear least squares optimization problem, which can be easily scaled to large models without introducing extra parameters beyond standard supervised learning. The straight paths are special and preferred because they are the shortest paths between two points, and can be simulated exactly without time discretization and hence yield computationally efficient models. We show that the procedure of learning a rectified flow from data, called rectification, turns an arbitrary coupling of \pi_0 and \pi_1 to a new deterministic coupling with provably non-increasing convex transport costs. In addition, recursively applying rectification allows us to obtain a sequence of flows with increasingly straight paths, which can be simulated accurately with coarse time discretization in the inference phase. In empirical studies, we show that rectified flow performs superbly on image generation, image-to-image translation, and domain adaptation. In particular, on image generation and translation, our method yields nearly straight flows that give high quality results even with a single Euler discretization step.

Diffusion models have emerged as a powerful tool for point cloud generation. A key component that drives the impressive performance for generating high-quality samples from noise is iteratively denoise for thousands of steps. While beneficial, the complexity of learning steps has limited its applications to many 3D real-world. To address this limitation, we propose Point Straight Flow (PSF), a model that exhibits impressive performance using one step. Our idea is based on the reformulation of the standard diffusion model, which optimizes the curvy learning trajectory into a straight path. Further, we develop a distillation strategy to shorten the straight path into one step without a performance loss, enabling applications to 3D real-world with latency constraints. We perform evaluations on multiple 3D tasks and find that our PSF performs comparably to the standard diffusion model, outperforming other efficient 3D point cloud generation methods. On real-world applications such as point cloud completion and training-free text-guided generation in a low-latency setup, PSF performs favorably.

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.

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.

The prediction of ship trajectories is a growing field of study in artificial intelligence. Traditional methods rely on the use of LSTM, GRU networks, and even Transformer architectures for the prediction of spatio-temporal series. This study proposes a viable alternative for predicting these trajectories using only GNSS positions. It considers this spatio-temporal problem as a natural language processing problem. The latitude/longitude coordinates of AIS messages are transformed into cell identifiers using the H3 index. Thanks to the pseudo-octal representation, it becomes easier for language models to learn the spatial hierarchy of the H3 index. The method is compared with a classical Kalman filter, widely used in the maritime domain, and introduces the Fr\'echet distance as the main evaluation metric. We show that it is possible to predict ship trajectories quite precisely up to 8 hours with 30 minutes of context. We demonstrate that this alternative works well enough to predict trajectories worldwide.

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 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.

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

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.

Automated Vehicles (AVs) promise significant advances in transportation. Critical to these improvements is understanding AVs' longitudinal behavior, relying heavily on real-world trajectory data. Existing open-source trajectory datasets of AV, however, often fall short in refinement, reliability, and completeness, hindering effective performance metrics analysis and model development. This study addresses these challenges by creating a Unified Longitudinal TRAjectory dataset for AVs (Ultra-AV) to analyze their microscopic longitudinal driving behaviors. This dataset compiles data from 13 distinct sources, encompassing various AV types, test sites, and experiment scenarios. We established a three-step data processing: 1. extraction of longitudinal trajectory data, 2. general data cleaning, and 3. data-specific cleaning to obtain the longitudinal trajectory data and car-following trajectory data. The validity of the processed data is affirmed through performance evaluations across safety, mobility, stability, and sustainability, along with an analysis of the relationships between variables in car-following models. Our work not only furnishes researchers with standardized data and metrics for longitudinal AV behavior studies but also sets guidelines for data collection and model development.

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.

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 .

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.

Model-based deep learning has achieved astounding successes due in part to the availability of large-scale real-world data. However, processing such massive amounts of data comes at a considerable cost in terms of computations, storage, training and the search for good neural architectures. Dataset distillation has thus recently come to the fore. This paradigm involves distilling information from large real-world datasets into tiny and compact synthetic datasets such that processing the latter ideally yields similar performances as the former. State-of-the-art methods primarily rely on learning the synthetic dataset by matching the gradients obtained during training between the real and synthetic data. However, these gradient-matching methods suffer from the so-called accumulated trajectory error caused by the discrepancy between the distillation and subsequent evaluation. To mitigate the adverse impact of this accumulated trajectory error, we propose a novel approach that encourages the optimization algorithm to seek a flat trajectory. We show that the weights trained on synthetic data are robust against the accumulated errors perturbations with the regularization towards the flat trajectory. Our method, called Flat Trajectory Distillation (FTD), is shown to boost the performance of gradient-matching methods by up to 4.7% on a subset of images of the ImageNet dataset with higher resolution images. We also validate the effectiveness and generalizability of our method with datasets of different resolutions and demonstrate its applicability to neural architecture search. Code is available at https://github.com/AngusDujw/FTD-distillation.

A significant number of traffic crashes are secondary crashes that occur because of an earlier incident on the road. Thus, early detection of traffic incidents is crucial for road users from safety perspectives with a potential to reduce the risk of secondary crashes. The wide availability of GPS devices now-a-days gives an opportunity of tracking and recording vehicle trajectories. The objective of this study is to use vehicle trajectory data for advance real-time detection of traffic incidents on highways using machine learning-based algorithms. The study uses three days of unevenly sequenced vehicle trajectory data and traffic incident data on I-10, one of the most crash-prone highways in Louisiana. Vehicle trajectories are converted to trajectories based on virtual detector locations to maintain spatial uniformity as well as to generate historical traffic data for machine learning algorithms. Trips matched with traffic incidents on the way are separated and along with other trips with similar spatial attributes are used to build a database for modeling. Multiple machine learning algorithms such as Logistic Regression, Random Forest, Extreme Gradient Boost, and Artificial Neural Network models are used to detect a trajectory that is likely to face an incident in the downstream road section. Results suggest that the Random Forest model achieves the best performance for predicting an incident with reasonable recall value and discrimination capability.

We present a new dataset, dedicated to the development of simultaneous localization and mapping methods for underwater vehicles navigating close to the seabed. The data sequences composing this dataset are recorded in three different environments: a harbor at a depth of a few meters, a first archaeological site at a depth of 270 meters and a second site at a depth of 380 meters. The data acquisition is performed using Remotely Operated Vehicles equipped with a monocular monochromatic camera, a low-cost inertial measurement unit, a pressure sensor and a computing unit, all embedded in a single enclosure. The sensors' measurements are recorded synchronously on the computing unit and seventeen sequences have been created from all the acquired data. These sequences are made available in the form of ROS bags and as raw data. For each sequence, a trajectory has also been computed offline using a Structure-from-Motion library in order to allow the comparison with real-time localization methods. With the release of this dataset, we wish to provide data difficult to acquire and to encourage the development of vision-based localization methods dedicated to the underwater environment. The dataset can be downloaded from: http://www.lirmm.fr/aqualoc/

Training long-horizon robotic policies in complex physical environments is essential for many applications, such as robotic manipulation. However, learning a policy that can generalize to unseen tasks is challenging. In this work, we propose to achieve one-shot task generalization by decoupling plan generation and plan execution. Specifically, our method solves complex long-horizon tasks in three steps: build a paired abstract environment by simplifying geometry and physics, generate abstract trajectories, and solve the original task by an abstract-to-executable trajectory translator. In the abstract environment, complex dynamics such as physical manipulation are removed, making abstract trajectories easier to generate. However, this introduces a large domain gap between abstract trajectories and the actual executed trajectories as abstract trajectories lack low-level details and are not aligned frame-to-frame with the executed trajectory. In a manner reminiscent of language translation, our approach leverages a seq-to-seq model to overcome the large domain gap between the abstract and executable trajectories, enabling the low-level policy to follow the abstract trajectory. Experimental results on various unseen long-horizon tasks with different robot embodiments demonstrate the practicability of our methods to achieve one-shot task generalization.

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.

Graphical User Interface (GUI) agents powered by Vision-Language Models (VLMs) have demonstrated human-like computer control capability. Despite their utility in advancing digital automation, a critical bottleneck persists: collecting high-quality trajectory data for training. Common practices for collecting such data rely on human supervision or synthetic data generation through executing pre-defined tasks, which are either resource-intensive or unable to guarantee data quality. Moreover, these methods suffer from limited data diversity and significant gaps between synthetic data and real-world environments. To address these challenges, we propose OS-Genesis, a novel GUI data synthesis pipeline that reverses the conventional trajectory collection process. Instead of relying on pre-defined tasks, OS-Genesis enables agents first to perceive environments and perform step-wise interactions, then retrospectively derive high-quality tasks to enable trajectory-level exploration. A trajectory reward model is then employed to ensure the quality of the generated trajectories. We demonstrate that training GUI agents with OS-Genesis significantly improves their performance on highly challenging online benchmarks. In-depth analysis further validates OS-Genesis's efficiency and its superior data quality and diversity compared to existing synthesis methods. Our codes, data, and checkpoints are available at https://qiushisun.github.io/OS-Genesis-Home/{OS-Genesis Homepage}.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Predicting the trajectories of road agents is essential for autonomous driving systems. The recent mainstream methods follow a static paradigm, which predicts the future trajectory by using a fixed duration of historical frames. These methods make the predictions independently even at adjacent time steps, which leads to potential instability and temporal inconsistency. As successive time steps have largely overlapping historical frames, their forecasting should have intrinsic correlation, such as overlapping predicted trajectories should be consistent, or be different but share the same motion goal depending on the road situation. Motivated by this, in this work, we introduce HPNet, a novel dynamic trajectory forecasting method. Aiming for stable and accurate trajectory forecasting, our method leverages not only historical frames including maps and agent states, but also historical predictions. Specifically, we newly design a Historical Prediction Attention module to automatically encode the dynamic relationship between successive predictions. Besides, it also extends the attention range beyond the currently visible window benefitting from the use of historical predictions. The proposed Historical Prediction Attention together with the Agent Attention and Mode Attention is further formulated as the Triple Factorized Attention module, serving as the core design of HPNet.Experiments on the Argoverse and INTERACTION datasets show that HPNet achieves state-of-the-art performance, and generates accurate and stable future trajectories. Our code are available at https://github.com/XiaolongTang23/HPNet.

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.

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.

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.

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

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.

Accurate prediction of pedestrians' future motions is critical for intelligent driving systems. Developing models for this task requires rich datasets containing diverse sets of samples. However, the existing naturalistic trajectory prediction datasets are generally imbalanced in favor of simpler samples and lack challenging scenarios. Such a long-tail effect causes prediction models to underperform on the tail portion of the data distribution containing safety-critical scenarios. Previous methods tackle the long-tail problem using methods such as contrastive learning and class-conditioned hypernetworks. These approaches, however, are not modular and cannot be applied to many machine learning architectures. In this work, we propose a modular model-agnostic framework for trajectory prediction that leverages a specialized mixture of experts. In our approach, each expert is trained with a specialized skill with respect to a particular part of the data. To produce predictions, we utilise a router network that selects the best expert by generating relative confidence scores. We conduct experimentation on common pedestrian trajectory prediction datasets and show that besides achieving state-of-the-art performance, our method significantly performs better on long-tail scenarios. We further conduct ablation studies to highlight the contribution of different proposed components.

We present a method for controlling a simulated humanoid to grasp an object and move it to follow an object trajectory. Due to the challenges in controlling a humanoid with dexterous hands, prior methods often use a disembodied hand and only consider vertical lifts or short trajectories. This limited scope hampers their applicability for object manipulation required for animation and simulation. To close this gap, we learn a controller that can pick up a large number (>1200) of objects and carry them to follow randomly generated trajectories. Our key insight is to leverage a humanoid motion representation that provides human-like motor skills and significantly speeds up training. Using only simplistic reward, state, and object representations, our method shows favorable scalability on diverse object and trajectories. For training, we do not need dataset of paired full-body motion and object trajectories. At test time, we only require the object mesh and desired trajectories for grasping and transporting. To demonstrate the capabilities of our method, we show state-of-the-art success rates in following object trajectories and generalizing to unseen objects. Code and models will be released.

This paper presents the development of a comprehensive dataset capturing interactions between Autonomous Vehicles (AVs) and traffic control devices, specifically traffic lights and stop signs. Derived from the Waymo Motion dataset, our work addresses a critical gap in the existing literature by providing real-world trajectory data on how AVs navigate these traffic control devices. We propose a methodology for identifying and extracting relevant interaction trajectory data from the Waymo Motion dataset, incorporating over 37,000 instances with traffic lights and 44,000 with stop signs. Our methodology includes defining rules to identify various interaction types, extracting trajectory data, and applying a wavelet-based denoising method to smooth the acceleration and speed profiles and eliminate anomalous values, thereby enhancing the trajectory quality. Quality assessment metrics indicate that trajectories obtained in this study have anomaly proportions in acceleration and jerk profiles reduced to near-zero levels across all interaction categories. By making this dataset publicly available, we aim to address the current gap in datasets containing AV interaction behaviors with traffic lights and signs. Based on the organized and published dataset, we can gain a more in-depth understanding of AVs' behavior when interacting with traffic lights and signs. This will facilitate research on AV integration into existing transportation infrastructures and networks, supporting the development of more accurate behavioral models and simulation tools.

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.

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.

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.

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.

We introduce WonderJourney, a modularized framework for perpetual 3D scene generation. Unlike prior work on view generation that focuses on a single type of scenes, we start at any user-provided location (by a text description or an image) and generate a journey through a long sequence of diverse yet coherently connected 3D scenes. We leverage an LLM to generate textual descriptions of the scenes in this journey, a text-driven point cloud generation pipeline to make a compelling and coherent sequence of 3D scenes, and a large VLM to verify the generated scenes. We show compelling, diverse visual results across various scene types and styles, forming imaginary "wonderjourneys". Project website: https://kovenyu.com/WonderJourney/

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 .

In Reinforcement Learning (RL), an agent acts in an unknown environment to maximize the expected cumulative discounted sum of an external reward signal, i.e., the expected return. In practice, in many tasks of interest, such as policy optimization, the agent usually spends its interaction budget by collecting episodes of fixed length within a simulator (i.e., Monte Carlo simulation). However, given the discounted nature of the RL objective, this data collection strategy might not be the best option. Indeed, the rewards taken in early simulation steps weigh exponentially more than future rewards. Taking a cue from this intuition, in this paper, we design an a-priori budget allocation strategy that leads to the collection of trajectories of different lengths, i.e., truncated. The proposed approach provably minimizes the width of the confidence intervals around the empirical estimates of the expected return of a policy. After discussing the theoretical properties of our method, we make use of our trajectory truncation mechanism to extend Policy Optimization via Importance Sampling (POIS, Metelli et al., 2018) algorithm. Finally, we conduct a numerical comparison between our algorithm and POIS: the results are consistent with our theory and show that an appropriate truncation of the trajectories can succeed in improving performance.

We present a publicly-available toolkit of flight-proven hardware and software to retrieve 5 TB of data or small physical samples from a stratospheric balloon platform. Before launch, a capsule is attached to the balloon, and rises with it. Upon remote command, the capsule is released and descends via parachute, continuously transmitting its location. Software to predict the trajectory can be used to select a safe but accessible landing site. We dropped two such capsules from the SuperBIT telescope, in September 2019. The capsules took ~37 minutes to descend from ~30 km altitude. They drifted 32 km and 19 km horizontally, but landed within 300 m and 600 m of their predicted landing sites. We found them easily, and successfully recovered the data. We welcome interest from other balloon teams for whom the technology would be useful.

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.

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.

Advances in time-resolved Particle Tracking Velocimetry (4D-PTV) techniques have been consistently revealed more accurate Lagrangian particle motions. A novel track initialisation technique as a complementary part of 4D-PTV, based on local temporal and spatial coherency of neighbour trajectories, is proposed. The proposed Lagrangian Coherent Track Initialisation (LCTI) applies physics-based Finite Time Lyapunov Exponent (FTLE) to build four frame coherent tracks. We locally determine the boundaries (i.e., ridges) of Lagrangian Coherent Structures (LCS) among neighbour trajectories by using FTLE to distinguish clusters of coherent motions. To evaluate the proposed technique, we created an open-access synthetic Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900 obtained from 3D Direct Numerical Simulation (DNS). The dataset is available to the public. Performance of the proposed method based on three characteristic parameters, temporal scale, particle concentration (i.e., density), and noise ratio, showed robust behaviour in finding true tracks compared to the recent initialisation algorithms. Sensitivity of LCTI to the number of untracked and wrong tracks are also discussed. We address the capability of using the proposed method as a function of a 4D-PTV scheme in the Lagrangian Particle Tracking challenge for a flow with high particle densities. Finally, the LCTI behaviour was assessed in a real jet impingement experiment. LCTI was found to be a reliable tracking tool in complex flow motions, with a strength revealed for flows with high particle concentrations.

We present MovingParts, a NeRF-based method for dynamic scene reconstruction and part discovery. We consider motion as an important cue for identifying parts, that all particles on the same part share the common motion pattern. From the perspective of fluid simulation, existing deformation-based methods for dynamic NeRF can be seen as parameterizing the scene motion under the Eulerian view, i.e., focusing on specific locations in space through which the fluid flows as time passes. However, it is intractable to extract the motion of constituting objects or parts using the Eulerian view representation. In this work, we introduce the dual Lagrangian view and enforce representations under the Eulerian/Lagrangian views to be cycle-consistent. Under the Lagrangian view, we parameterize the scene motion by tracking the trajectory of particles on objects. The Lagrangian view makes it convenient to discover parts by factorizing the scene motion as a composition of part-level rigid motions. Experimentally, our method can achieve fast and high-quality dynamic scene reconstruction from even a single moving camera, and the induced part-based representation allows direct applications of part tracking, animation, 3D scene editing, etc.

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

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.

3D multi-object tracking (MOT) is vital for many applications including autonomous driving vehicles and service robots. With the commonly used tracking-by-detection paradigm, 3D MOT has made important progress in recent years. However, these methods only use the detection boxes of the current frame to obtain trajectory-box association results, which makes it impossible for the tracker to recover objects missed by the detector. In this paper, we present TrajectoryFormer, a novel point-cloud-based 3D MOT framework. To recover the missed object by detector, we generates multiple trajectory hypotheses with hybrid candidate boxes, including temporally predicted boxes and current-frame detection boxes, for trajectory-box association. The predicted boxes can propagate object's history trajectory information to the current frame and thus the network can tolerate short-term miss detection of the tracked objects. We combine long-term object motion feature and short-term object appearance feature to create per-hypothesis feature embedding, which reduces the computational overhead for spatial-temporal encoding. Additionally, we introduce a Global-Local Interaction Module to conduct information interaction among all hypotheses and models their spatial relations, leading to accurate estimation of hypotheses. Our TrajectoryFormer achieves state-of-the-art performance on the Waymo 3D MOT benchmarks. Code is available at https://github.com/poodarchu/EFG .

Training deep neural networks (DNNs) is computationally expensive, which is problematic especially when performing duplicated or similar training runs in model ensemble or fine-tuning pre-trained models, for example. Once we have trained one DNN on some dataset, we have its learning trajectory (i.e., a sequence of intermediate parameters during training) which may potentially contain useful information for learning the dataset. However, there has been no attempt to utilize such information of a given learning trajectory for another training. In this paper, we formulate the problem of "transferring" a given learning trajectory from one initial parameter to another one (learning transfer problem) and derive the first algorithm to approximately solve it by matching gradients successively along the trajectory via permutation symmetry. We empirically show that the transferred parameters achieve non-trivial accuracy before any direct training, and can be trained significantly faster than training from scratch.

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy).

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.

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

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal goal-reaching strategies are rarely reversible (symmetrical). Distance functions supported on these asymmetrical structures are called quasimetrics. Despite their common appearance, little research has been done on the learning of quasimetrics. Our theoretical analysis reveals that a common class of learning algorithms, including unconstrained multilayer perceptrons (MLPs), provably fails to learn a quasimetric consistent with training data. In contrast, our proposed Poisson Quasimetric Embedding (PQE) is the first quasimetric learning formulation that both is learnable with gradient-based optimization and enjoys strong performance guarantees. Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines.

Trajectory prediction plays an important role in various applications, including autonomous driving, robotics, and scene understanding. Existing approaches mainly focus on developing compact neural networks to increase prediction precision on public datasets, typically employing a standardized input duration. However, a notable issue arises when these models are evaluated with varying observation lengths, leading to a significant performance drop, a phenomenon we term the Observation Length Shift. To address this issue, we introduce a general and effective framework, the FlexiLength Network (FLN), to enhance the robustness of existing trajectory prediction techniques against varying observation periods. Specifically, FLN integrates trajectory data with diverse observation lengths, incorporates FlexiLength Calibration (FLC) to acquire temporal invariant representations, and employs FlexiLength Adaptation (FLA) to further refine these representations for more accurate future trajectory predictions. Comprehensive experiments on multiple datasets, ie, ETH/UCY, nuScenes, and Argoverse 1, demonstrate the effectiveness and flexibility of our proposed FLN framework.

Dataset Distillation is used to create a concise, yet informative, synthetic dataset that can replace the original dataset for training purposes. Some leading methods in this domain prioritize long-range matching, involving the unrolling of training trajectories with a fixed number of steps (NS) on the synthetic dataset to align with various expert training trajectories. However, traditional long-range matching methods possess an overfitting-like problem, the fixed step size NS forces synthetic dataset to distortedly conform seen expert training trajectories, resulting in a loss of generality-especially to those from unencountered architecture. We refer to this as the Accumulated Mismatching Problem (AMP), and propose a new approach, Automatic Training Trajectories (ATT), which dynamically and adaptively adjusts trajectory length NS to address the AMP. Our method outperforms existing methods particularly in tests involving cross-architectures. Moreover, owing to its adaptive nature, it exhibits enhanced stability in the face of parameter variations.

Latent Consistency Model (LCM) extends the Consistency Model to the latent space and leverages the guided consistency distillation technique to achieve impressive performance in accelerating text-to-image synthesis. However, we observed that LCM struggles to generate images with both clarity and detailed intricacy. To address this limitation, we initially delve into and elucidate the underlying causes. Our investigation identifies that the primary issue stems from errors in three distinct areas. Consequently, we introduce Trajectory Consistency Distillation (TCD), which encompasses trajectory consistency function and strategic stochastic sampling. The trajectory consistency function diminishes the distillation errors by broadening the scope of the self-consistency boundary condition and endowing the TCD with the ability to accurately trace the entire trajectory of the Probability Flow ODE. Additionally, strategic stochastic sampling is specifically designed to circumvent the accumulated errors inherent in multi-step consistency sampling, which is meticulously tailored to complement the TCD model. Experiments demonstrate that TCD not only significantly enhances image quality at low NFEs but also yields more detailed results compared to the teacher model at high NFEs.

Controllable video generation has gained significant attention in recent years. However, two main limitations persist: Firstly, most existing works focus on either text, image, or trajectory-based control, leading to an inability to achieve fine-grained control in videos. Secondly, trajectory control research is still in its early stages, with most experiments being conducted on simple datasets like Human3.6M. This constraint limits the models' capability to process open-domain images and effectively handle complex curved trajectories. In this paper, we propose DragNUWA, an open-domain diffusion-based video generation model. To tackle the issue of insufficient control granularity in existing works, we simultaneously introduce text, image, and trajectory information to provide fine-grained control over video content from semantic, spatial, and temporal perspectives. To resolve the problem of limited open-domain trajectory control in current research, We propose trajectory modeling with three aspects: a Trajectory Sampler (TS) to enable open-domain control of arbitrary trajectories, a Multiscale Fusion (MF) to control trajectories in different granularities, and an Adaptive Training (AT) strategy to generate consistent videos following trajectories. Our experiments validate the effectiveness of DragNUWA, demonstrating its superior performance in fine-grained control in video generation. The homepage link is https://www.microsoft.com/en-us/research/project/dragnuwa/

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.

Tracking by detection has been the prevailing paradigm in the field of Multi-object Tracking (MOT). These methods typically rely on the Kalman Filter to estimate the future locations of objects, assuming linear object motion. However, they fall short when tracking objects exhibiting nonlinear and diverse motion in scenarios like dancing and sports. In addition, there has been limited focus on utilizing learning-based motion predictors in MOT. To address these challenges, we resort to exploring data-driven motion prediction methods. Inspired by the great expectation of state space models (SSMs), such as Mamba, in long-term sequence modeling with near-linear complexity, we introduce a Mamba-based motion model named Mamba moTion Predictor (MTP). MTP is designed to model the complex motion patterns of objects like dancers and athletes. Specifically, MTP takes the spatial-temporal location dynamics of objects as input, captures the motion pattern using a bi-Mamba encoding layer, and predicts the next motion. In real-world scenarios, objects may be missed due to occlusion or motion blur, leading to premature termination of their trajectories. To tackle this challenge, we further expand the application of MTP. We employ it in an autoregressive way to compensate for missing observations by utilizing its own predictions as inputs, thereby contributing to more consistent trajectories. Our proposed tracker, MambaTrack, demonstrates advanced performance on benchmarks such as Dancetrack and SportsMOT, which are characterized by complex motion and severe occlusion.

We study the joint image of lines incident to points, meaning the set of image tuples obtained from fixed cameras observing a varying 3D point-line incidence. We prove a formula for the number of complex critical points of the triangulation problem that aims to compute a 3D point-line incidence from noisy images. Our formula works for an arbitrary number of images and measures the intrinsic difficulty of this triangulation. Additionally, we conduct numerical experiments using homotopy continuation methods, comparing different approaches of triangulation of such incidences. In our setup, exploiting the incidence relations gives both a faster point reconstruction and in three views more accurate.

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.

In this work, we propose a training-free, trajectory-based controllable T2I approach, termed TraDiffusion. This novel method allows users to effortlessly guide image generation via mouse trajectories. To achieve precise control, we design a distance awareness energy function to effectively guide latent variables, ensuring that the focus of generation is within the areas defined by the trajectory. The energy function encompasses a control function to draw the generation closer to the specified trajectory and a movement function to diminish activity in areas distant from the trajectory. Through extensive experiments and qualitative assessments on the COCO dataset, the results reveal that TraDiffusion facilitates simpler, more natural image control. Moreover, it showcases the ability to manipulate salient regions, attributes, and relationships within the generated images, alongside visual input based on arbitrary or enhanced trajectories.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

In this work, we propose a novel Trajectory Score Matching (TSM) method that aims to solve the pseudo ground truth inconsistency problem caused by the accumulated error in Interval Score Matching (ISM) when using the Denoising Diffusion Implicit Models (DDIM) inversion process. Unlike ISM which adopts the inversion process of DDIM to calculate on a single path, our TSM method leverages the inversion process of DDIM to generate two paths from the same starting point for calculation. Since both paths start from the same starting point, TSM can reduce the accumulated error compared to ISM, thus alleviating the problem of pseudo ground truth inconsistency. TSM enhances the stability and consistency of the model's generated paths during the distillation process. We demonstrate this experimentally and further show that ISM is a special case of TSM. Furthermore, to optimize the current multi-stage optimization process from high-resolution text to 3D generation, we adopt Stable Diffusion XL for guidance. In response to the issues of abnormal replication and splitting caused by unstable gradients during the 3D Gaussian splatting process when using Stable Diffusion XL, we propose a pixel-by-pixel gradient clipping method. Extensive experiments show that our model significantly surpasses the state-of-the-art models in terms of visual quality and performance. Code: https://github.com/xingy038/Dreamer-XL.

Predicting future trajectories for other road agents is an essential task for autonomous vehicles. Established trajectory prediction methods primarily use agent tracks generated by a detection and tracking system and HD map as inputs. In this work, we propose a novel method that also incorporates visual input from surround-view cameras, allowing the model to utilize visual cues such as human gazes and gestures, road conditions, vehicle turn signals, etc, which are typically hidden from the model in prior methods. Furthermore, we use textual descriptions generated by a Vision-Language Model (VLM) and refined by a Large Language Model (LLM) as supervision during training to guide the model on what to learn from the input data. Despite using these extra inputs, our method achieves a latency of 53 ms, making it feasible for real-time processing, which is significantly faster than that of previous single-agent prediction methods with similar performance. Our experiments show that both the visual inputs and the textual descriptions contribute to improvements in trajectory prediction performance, and our qualitative analysis highlights how the model is able to exploit these additional inputs. Lastly, in this work we create and release the nuScenes-Text dataset, which augments the established nuScenes dataset with rich textual annotations for every scene, demonstrating the positive impact of utilizing VLM on trajectory prediction. Our project page is at https://moonseokha.github.io/VisionTrap/

This paper introduces Elastic Decision Transformer (EDT), a significant advancement over the existing Decision Transformer (DT) and its variants. Although DT purports to generate an optimal trajectory, empirical evidence suggests it struggles with trajectory stitching, a process involving the generation of an optimal or near-optimal trajectory from the best parts of a set of sub-optimal trajectories. The proposed EDT differentiates itself by facilitating trajectory stitching during action inference at test time, achieved by adjusting the history length maintained in DT. Further, the EDT optimizes the trajectory by retaining a longer history when the previous trajectory is optimal and a shorter one when it is sub-optimal, enabling it to "stitch" with a more optimal trajectory. Extensive experimentation demonstrates EDT's ability to bridge the performance gap between DT-based and Q Learning-based approaches. In particular, the EDT outperforms Q Learning-based methods in a multi-task regime on the D4RL locomotion benchmark and Atari games. Videos are available at: https://kristery.github.io/edt/

Diffusion model has demonstrated remarkable capability in video generation, which further sparks interest in introducing trajectory control into the generation process. While existing works mainly focus on training-based methods (e.g., conditional adapter), we argue that diffusion model itself allows decent control over the generated content without requiring any training. In this study, we introduce a tuning-free framework to achieve trajectory-controllable video generation, by imposing guidance on both noise construction and attention computation. Specifically, 1) we first show several instructive phenomenons and analyze how initial noises influence the motion trajectory of generated content. 2) Subsequently, we propose FreeTraj, a tuning-free approach that enables trajectory control by modifying noise sampling and attention mechanisms. 3) Furthermore, we extend FreeTraj to facilitate longer and larger video generation with controllable trajectories. Equipped with these designs, users have the flexibility to provide trajectories manually or opt for trajectories automatically generated by the LLM trajectory planner. Extensive experiments validate the efficacy of our approach in enhancing the trajectory controllability of video diffusion models.

This paper explores the problem of collision-free motion generation for manipulators by formulating it as a global motion optimization problem. We develop a parallel optimization technique to solve this problem and demonstrate its effectiveness on massively parallel GPUs. We show that combining simple optimization techniques with many parallel seeds leads to solving difficult motion generation problems within 50ms on average, 60x faster than state-of-the-art (SOTA) trajectory optimization methods. We achieve SOTA performance by combining L-BFGS step direction estimation with a novel parallel noisy line search scheme and a particle-based optimization solver. To further aid trajectory optimization, we develop a parallel geometric planner that plans within 20ms and also introduce a collision-free IK solver that can solve over 7000 queries/s. We package our contributions into a state of the art GPU accelerated motion generation library, cuRobo and release it to enrich the robotics community. Additional details are available at https://curobo.org

Animating clipart images with seamless motion while maintaining visual fidelity and temporal coherence presents significant challenges. Existing methods, such as AniClipart, effectively model spatial deformations but often fail to ensure smooth temporal transitions, resulting in artifacts like abrupt motions and geometric distortions. Similarly, text-to-video (T2V) and image-to-video (I2V) models struggle to handle clipart due to the mismatch in statistical properties between natural video and clipart styles. This paper introduces FlexiClip, a novel approach designed to overcome these limitations by addressing the intertwined challenges of temporal consistency and geometric integrity. FlexiClip extends traditional B\'ezier curve-based trajectory modeling with key innovations: temporal Jacobians to correct motion dynamics incrementally, continuous-time modeling via probability flow ODEs (pfODEs) to mitigate temporal noise, and a flow matching loss inspired by GFlowNet principles to optimize smooth motion transitions. These enhancements ensure coherent animations across complex scenarios involving rapid movements and non-rigid deformations. Extensive experiments validate the effectiveness of FlexiClip in generating animations that are not only smooth and natural but also structurally consistent across diverse clipart types, including humans and animals. By integrating spatial and temporal modeling with pre-trained video diffusion models, FlexiClip sets a new standard for high-quality clipart animation, offering robust performance across a wide range of visual content. Project Page: https://creative-gen.github.io/flexiclip.github.io/

Object goal navigation aims to navigate an agent to locations of a given object category in unseen environments. Classical methods explicitly build maps of environments and require extensive engineering while lacking semantic information for object-oriented exploration. On the other hand, end-to-end learning methods alleviate manual map design and predict actions using implicit representations. Such methods, however, lack an explicit notion of geometry and may have limited ability to encode navigation history. In this work, we propose an implicit spatial map for object goal navigation. Our implicit map is recursively updated with new observations at each step using a transformer. To encourage spatial reasoning, we introduce auxiliary tasks and train our model to reconstruct explicit maps as well as to predict visual features, semantic labels and actions. Our method significantly outperforms the state of the art on the challenging MP3D dataset and generalizes well to the HM3D dataset. We successfully deploy our model on a real robot and achieve encouraging object goal navigation results in real scenes using only a few real-world demonstrations. Code, trained models and videos are available at https://www.di.ens.fr/willow/research/onav_rim/.

Coordinated flight of multiple drones allows to achieve tasks faster such as search and rescue and infrastructure inspection. Thus, pushing the state-of-the-art of aerial swarms in navigation speed and robustness is of tremendous benefit. In particular, being able to account for unexplored/unknown environments when planning trajectories allows for safer flight. In this work, we propose the first high-speed, decentralized, and synchronous motion planning framework (HDSM) for an aerial swarm that explicitly takes into account the unknown/undiscovered parts of the environment. The proposed approach generates an optimized trajectory for each planning agent that avoids obstacles and other planning agents while moving and exploring the environment. The only global information that each agent has is the target location. The generated trajectory is high-speed, safe from unexplored spaces, and brings the agent closer to its goal. The proposed method outperforms four recent state-of-the-art methods in success rate (100% success in reaching the target location), flight speed (67% faster), and flight time (42% lower). Finally, the method is validated on a set of Crazyflie nano-drones as a proof of concept.

We present a novel framework for motion forecasting with Dual Consistency Constraints and Multi-Pseudo-Target supervision. The motion forecasting task predicts future trajectories of vehicles by incorporating spatial and temporal information from the past. A key design of DCMS is the proposed Dual Consistency Constraints that regularize the predicted trajectories under spatial and temporal perturbation during the training stage. In addition, we design a novel self-ensembling scheme to obtain accurate pseudo targets to model the multi-modality in motion forecasting through supervision with multiple targets explicitly, namely Multi-Pseudo-Target supervision. Our experimental results on the Argoverse motion forecasting benchmark show that DCMS significantly outperforms the state-of-the-art methods, achieving 1st place on the leaderboard. We also demonstrate that our proposed strategies can be incorporated into other motion forecasting approaches as general training schemes.

Trajectory data, which tracks movements through geographic locations, is crucial for improving real-world applications. However, collecting such sensitive data raises considerable privacy concerns. Local differential privacy (LDP) offers a solution by allowing individuals to locally perturb their trajectory data before sharing it. Despite its privacy benefits, LDP protocols are vulnerable to data poisoning attacks, where attackers inject fake data to manipulate aggregated results. In this work, we make the first attempt to analyze vulnerabilities in several representative LDP trajectory protocols. We propose TraP, a heuristic algorithm for data Poisoning attacks using a prefix-suffix method to optimize fake Trajectory selection, significantly reducing computational complexity. Our experimental results demonstrate that our attack can substantially increase target pattern occurrences in the perturbed trajectory dataset with few fake users. This study underscores the urgent need for robust defenses and better protocol designs to safeguard LDP trajectory data against malicious manipulation.

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

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

This paper presents a Simple and effIcient Motion Prediction baseLine (SIMPL) for autonomous vehicles. Unlike conventional agent-centric methods with high accuracy but repetitive computations and scene-centric methods with compromised accuracy and generalizability, SIMPL delivers real-time, accurate motion predictions for all relevant traffic participants. To achieve improvements in both accuracy and inference speed, we propose a compact and efficient global feature fusion module that performs directed message passing in a symmetric manner, enabling the network to forecast future motion for all road users in a single feed-forward pass and mitigating accuracy loss caused by viewpoint shifting. Additionally, we investigate the continuous trajectory parameterization using Bernstein basis polynomials in trajectory decoding, allowing evaluations of states and their higher-order derivatives at any desired time point, which is valuable for downstream planning tasks. As a strong baseline, SIMPL exhibits highly competitive performance on Argoverse 1 & 2 motion forecasting benchmarks compared with other state-of-the-art methods. Furthermore, its lightweight design and low inference latency make SIMPL highly extensible and promising for real-world onboard deployment. We open-source the code at https://github.com/HKUST-Aerial-Robotics/SIMPL.

In the present study, we extend the approach of the wake field conformal mapping technique to the case of the step transition and a collimator. We assume that all pipes have different arbitrary cross-sectional shapes. We derive simple analytical expressions for the lower and upper bounds of both longitudinal and transverse wake potentials. We test the derived expressions against well-known formulas in several representative examples. The proposed method can greatly simplify the optimization of collimating sections as well as become a useful tool in the exploration of transverse beam shaping ideas.

Recent advancements in 3D generation have leveraged synthetic datasets with ground truth 3D assets and predefined cameras. However, the potential of adopting real-world datasets, which can produce significantly more realistic 3D scenes, remains largely unexplored. In this work, we delve into the key challenge of the complex and scene-specific camera trajectories found in real-world captures. We introduce Director3D, a robust open-world text-to-3D generation framework, designed to generate both real-world 3D scenes and adaptive camera trajectories. To achieve this, (1) we first utilize a Trajectory Diffusion Transformer, acting as the Cinematographer, to model the distribution of camera trajectories based on textual descriptions. (2) Next, a Gaussian-driven Multi-view Latent Diffusion Model serves as the Decorator, modeling the image sequence distribution given the camera trajectories and texts. This model, fine-tuned from a 2D diffusion model, directly generates pixel-aligned 3D Gaussians as an immediate 3D scene representation for consistent denoising. (3) Lastly, the 3D Gaussians are refined by a novel SDS++ loss as the Detailer, which incorporates the prior of the 2D diffusion model. Extensive experiments demonstrate that Director3D outperforms existing methods, offering superior performance in real-world 3D generation.

We introduce DragAnything, which utilizes a entity representation to achieve motion control for any object in controllable video generation. Comparison to existing motion control methods, DragAnything offers several advantages. Firstly, trajectory-based is more userfriendly for interaction, when acquiring other guidance signals (e.g., masks, depth maps) is labor-intensive. Users only need to draw a line (trajectory) during interaction. Secondly, our entity representation serves as an open-domain embedding capable of representing any object, enabling the control of motion for diverse entities, including background. Lastly, our entity representation allows simultaneous and distinct motion control for multiple objects. Extensive experiments demonstrate that our DragAnything achieves state-of-the-art performance for FVD, FID, and User Study, particularly in terms of object motion control, where our method surpasses the previous methods (e.g., DragNUWA) by 26% in human voting.

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

Flying Triangulation sensors enable a free-hand and motion-robust 3D data acquisition of complex shaped objects. The measurement principle is based on a multi-line light-sectioning approach and uses sophisticated algorithms for real-time registration (S. Ettl et al., Appl. Opt. 51 (2012) 281-289). As "single-shot principle", light sectioning enables the option to get surface data from one single camera exposure. But there is a drawback: A pixel-dense measurement is not possible because of fundamental information-theoretical reasons. By "pixel-dense" we understand that each pixel displays individually measured distance information, neither interpolated from its neighbour pixels nor using lateral context information. Hence, for monomodal single-shot principles, the 3D data generated from one 2D raw image display a significantly lower space-bandwidth than the camera permits. This is the price one must pay for motion robustness. Currently, our sensors project about 10 lines (each with 1000 pixels), reaching an considerable lower data efficiency than theoretically possible for a single-shot sensor. Our aim is to push Flying Triangulation to its information-theoretical limits. Therefore, the line density as well as the measurement depth needs to be significantly increased. This causes serious indexing ambiguities. On the road to a single-shot 3D movie camera, we are working on solutions to overcome the problem of false line indexing by utilizing yet unexploited information. We will present several approaches and will discuss profound information-theoretical questions about the information efficiency of 3D sensors.

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

Human trajectory prediction is typically posed as a zero-shot generalization problem: a predictor is learnt on a dataset of human motion in training scenes, and then deployed on unseen test scenes. While this paradigm has yielded tremendous progress, it fundamentally assumes that trends in human behavior within the deployment scene are constant over time. As such, current prediction models are unable to adapt to scene-specific transient human behaviors, such as crowds temporarily gathering to see buskers, pedestrians hurrying through the rain and avoiding puddles, or a protest breaking out. We formalize the problem of scene-specific adaptive trajectory prediction and propose a new adaptation approach inspired by prompt tuning called latent corridors. By augmenting the input of any pre-trained human trajectory predictor with learnable image prompts, the predictor can improve in the deployment scene by inferring trends from extremely small amounts of new data (e.g., 2 humans observed for 30 seconds). With less than 0.1% additional model parameters, we see up to 23.9% ADE improvement in MOTSynth simulated data and 16.4% ADE in MOT and Wildtrack real pedestrian data. Qualitatively, we observe that latent corridors imbue predictors with an awareness of scene geometry and scene-specific human behaviors that non-adaptive predictors struggle to capture. The project website can be found at https://neerja.me/atp_latent_corridors/.

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.

Animals are capable of extreme agility, yet understanding their complex dynamics, which have ecological, biomechanical and evolutionary implications, remains challenging. Being able to study this incredible agility will be critical for the development of next-generation autonomous legged robots. In particular, the cheetah (acinonyx jubatus) is supremely fast and maneuverable, yet quantifying its whole-body 3D kinematic data during locomotion in the wild remains a challenge, even with new deep learning-based methods. In this work we present an extensive dataset of free-running cheetahs in the wild, called AcinoSet, that contains 119,490 frames of multi-view synchronized high-speed video footage, camera calibration files and 7,588 human-annotated frames. We utilize markerless animal pose estimation to provide 2D keypoints. Then, we use three methods that serve as strong baselines for 3D pose estimation tool development: traditional sparse bundle adjustment, an Extended Kalman Filter, and a trajectory optimization-based method we call Full Trajectory Estimation. The resulting 3D trajectories, human-checked 3D ground truth, and an interactive tool to inspect the data is also provided. We believe this dataset will be useful for a diverse range of fields such as ecology, neuroscience, robotics, biomechanics as well as computer vision.

We address a benchmark task in agile robotics: catching objects thrown at high-speed. This is a challenging task that involves tracking, intercepting, and cradling a thrown object with access only to visual observations of the object and the proprioceptive state of the robot, all within a fraction of a second. We present the relative merits of two fundamentally different solution strategies: (i) Model Predictive Control using accelerated constrained trajectory optimization, and (ii) Reinforcement Learning using zeroth-order optimization. We provide insights into various performance trade-offs including sample efficiency, sim-to-real transfer, robustness to distribution shifts, and whole-body multimodality via extensive on-hardware experiments. We conclude with proposals on fusing "classical" and "learning-based" techniques for agile robot control. Videos of our experiments may be found at https://sites.google.com/view/agile-catching

Maritime transportation is paramount in achieving global economic growth, entailing concurrent ecological obligations in sustainability and safeguarding endangered marine species, most notably preserving large whale populations. In this regard, the Automatic Identification System (AIS) data plays a significant role by offering real-time streaming data on vessel movement, allowing enhanced traffic monitoring. This study explores using AIS data to prevent vessel-to-whale collisions by forecasting long-term vessel trajectories from engineered AIS data sequences. For such a task, we have developed an encoder-decoder model architecture using Bidirectional Long Short-Term Memory Networks (Bi-LSTM) to predict the next 12 hours of vessel trajectories using 1 to 3 hours of AIS data as input. We feed the model with probabilistic features engineered from historical AIS data that refer to each trajectory's potential route and destination. The model then predicts the vessel's trajectory, considering these additional features by leveraging convolutional layers for spatial feature learning and a position-aware attention mechanism that increases the importance of recent timesteps of a sequence during temporal feature learning. The probabilistic features have an F1 Score of approximately 85% and 75% for each feature type, respectively, demonstrating their effectiveness in augmenting information to the neural network. We test our model on the Gulf of St. Lawrence, a region known to be the habitat of North Atlantic Right Whales (NARW). Our model achieved a high R2 score of over 98% using various techniques and features. It stands out among other approaches as it can make complex decisions during turnings and path selection. Our study highlights the potential of data engineering and trajectory forecasting models for marine life species preservation.

The release of nuPlan marks a new era in vehicle motion planning research, offering the first large-scale real-world dataset and evaluation schemes requiring both precise short-term planning and long-horizon ego-forecasting. Existing systems struggle to simultaneously meet both requirements. Indeed, we find that these tasks are fundamentally misaligned and should be addressed independently. We further assess the current state of closed-loop planning in the field, revealing the limitations of learning-based methods in complex real-world scenarios and the value of simple rule-based priors such as centerline selection through lane graph search algorithms. More surprisingly, for the open-loop sub-task, we observe that the best results are achieved when using only this centerline as scene context (\ie, ignoring all information regarding the map and other agents). Combining these insights, we propose an extremely simple and efficient planner which outperforms an extensive set of competitors, winning the nuPlan planning challenge 2023.

This study seeks to automate camera movement control for filming existing subjects into attractive videos, contrasting with the creation of non-existent content by directly generating the pixels. We select drone videos as our test case due to their rich and challenging motion patterns, distinctive viewing angles, and precise controls. Existing AI videography methods struggle with limited appearance diversity in simulation training, high costs of recording expert operations, and difficulties in designing heuristic-based goals to cover all scenarios. To avoid these issues, we propose a scalable method that involves collecting real-world training data to improve diversity, extracting camera trajectories automatically to minimize annotation costs, and training an effective architecture that does not rely on heuristics. Specifically, we collect 99k high-quality trajectories by running 3D reconstruction on online videos, connecting camera poses from consecutive frames to formulate 3D camera paths, and using Kalman filter to identify and remove low-quality data. Moreover, we introduce DVGFormer, an auto-regressive transformer that leverages the camera path and images from all past frames to predict camera movement in the next frame. We evaluate our system across 38 synthetic natural scenes and 7 real city 3D scans. We show that our system effectively learns to perform challenging camera movements such as navigating through obstacles, maintaining low altitude to increase perceived speed, and orbiting towers and buildings, which are very useful for recording high-quality videos. Data and code are available at dvgformer.github.io.

Keypoint-based representation has proven advantageous in various visual and robotic tasks. However, the existing 2D and 3D methods for detecting keypoints mainly rely on geometric consistency to achieve spatial alignment, neglecting temporal consistency. To address this issue, the Transporter method was introduced for 2D data, which reconstructs the target frame from the source frame to incorporate both spatial and temporal information. However, the direct application of the Transporter to 3D point clouds is infeasible due to their structural differences from 2D images. Thus, we propose the first 3D version of the Transporter, which leverages hybrid 3D representation, cross attention, and implicit reconstruction. We apply this new learning system on 3D articulated objects and nonrigid animals (humans and rodents) and show that learned keypoints are spatio-temporally consistent. Additionally, we propose a closed-loop control strategy that utilizes the learned keypoints for 3D object manipulation and demonstrate its superior performance. Codes are available at https://github.com/zhongcl-thu/3D-Implicit-Transporter.