Daily Papers

Interactive video generation and editing are becoming increasingly important for creative design. In this report, we introduce EditStream: a unified framework for interactive video generation and editing. EditStream unifies multiple video creation and manipulation tasks within a single DiT-based model through flexible task-specific conditioning, and further transforms it into a fast, few-step autoregressive model for efficient streaming. It supports Text-to-Video, Image-to-Video, Video-to-Video, Editing Propagation, Reference-guided Video Editing, and Camera Pose Change, enabling flexible control over video generation, transformation, and editing within one system. To make the unified model practical for interactive use, we develop a two-stage distillation approach that combines Velocity Moment Matching (VMM) with autoregressive unrolling. VMM matches conditional velocity moments at student-reached intermediate states to preserve generation quality and motion, while unrolling exposes the student to its own autoregressive predictions to improve temporal stability. Together, they alleviate common challenges in few-step autoregressive video generation, including over-saturation, degraded motion, temporal instability, and complex training. EditStream provides a practical and scalable solution that bridges high-quality diffusion-based video models with interactive creative workflows.

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and solutions (or final states), enabling both forward simulation and inverse recovery with limited paired data. At inference, sampling is guided by a composite loss that enforces agreement with sparse measurements and reduces the PDE residual; we support deterministic, stochastic, and hybrid samplers. We provide error guarantees for these guided procedures. For the deterministic optimizer, a coercivity condition ensures trajectory boundedness and a phase-wise contraction yields logarithmic complexity in the target accuracy. For the stochastic sampler, we introduce adaptive guidance and assume dissipativity of the velocity field to obtain uniform moment bounds independent of the noise-floor parameter. This leads to polynomial-time error bounds, and a matching lower bound shows constant guidance induces an unavoidable positive bias, motivating adaptivity. A hybrid deterministic-stochastic analysis is also provided. Experiments on static and time-dependent benchmark PDEs demonstrate competitive accuracy and faster inference than diffusion-based generative models.

While Flow Matching theoretically guarantees constant-velocity trajectories, we identify a critical breakdown in high-dimensional practice: the Velocity Deficit. We show that the MSE objective systematically underestimates velocity magnitude, causing generated samples to fail to reach the data manifold-a phenomenon we term Integration Lag. To rectify this, we propose Initial Energy Injection, instantiated via two complementary methods: the training-based Magnitude-Aware Flow Matching (MAFM) and the training-free Scale Schedule Corrector (SSC). Both are grounded in our discovery of a crucial asymmetry: velocity contraction causes harmful kinetic stagnation at the trajectory's start, yet acts as a beneficial denoising mechanism at its end. Empirically, SSC yields significant efficiency gains with zero retraining and just one line of code. On ImageNet-1k (256x256), it improves FID by 44.6% (from 13.68 to 7.58) and achieves a 5x speedup, enabling a 50-step generator (FID 7.58) to beat a 250-step baseline (FID 8.65). Furthermore, our methods generalize to Text-to-Image tasks and high-resolution generation, improving FID on MS-COCO by ~22%.

Reward-based fine-tuning of diffusion models has largely inherited likelihood-based policy optimization developed for autoregressive large language models (LLMs). Diffusion models, however, are natively trained through velocity regression and do not directly provide the likelihood of a generated sample. Existing methods address this using transition likelihoods along stochastic denoising trajectories or evidence lower bounds (ELBOs) to approximate generated-sample likelihoods. These approximations arise from applying likelihood-based updates to models whose native training and generation operate through velocity fields. We instead take velocity matching as the starting point for reward fine-tuning. We propose reward-based velocity matching (RVM), which weights the velocity-matching loss by reward with an additional anchor regression term, requiring neither likelihood estimation nor likelihood ratios. RVM recovers Reinforce Adjoint Matching at the update level and contains DiffusionNFT as a special case, while ELBO-based methods are closely related through the same velocity-regression structure. This unified view isolates reward design and anchor velocity as principal design choices in velocity-based fine-tuning. Across text-to-image, text-to-video, and image-to-video generation, RVM matches or outperforms the evaluated trajectory-based methods. On Wan2.1-T2V-1.3B, it achieves the highest VBench Overall among the evaluated methods, with substantially lower estimated training costs than the trajectory-based approaches. For video fine-tuning, we introduce a dynamic-tracking reward that provides explicit motion feedback and improves both Dynamic Degree and overall VBench performance.

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fr\'echet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256times256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

While flow matching is elegant, its reliance on single-sample conditional velocities leads to high-variance training targets that destabilize optimization and slow convergence. By explicitly characterizing this variance, we identify 1) a high-variance regime near the prior, where optimization is challenging, and 2) a low-variance regime near the data distribution, where conditional and marginal velocities nearly coincide. Leveraging this insight, we propose Stable Velocity, a unified framework that improves both training and sampling. For training, we introduce Stable Velocity Matching (StableVM), an unbiased variance-reduction objective, along with Variance-Aware Representation Alignment (VA-REPA), which adaptively strengthen auxiliary supervision in the low-variance regime. For inference, we show that dynamics in the low-variance regime admit closed-form simplifications, enabling Stable Velocity Sampling (StableVS), a finetuning-free acceleration. Extensive experiments on ImageNet 256times256 and large pretrained text-to-image and text-to-video models, including SD3.5, Flux, Qwen-Image, and Wan2.2, demonstrate consistent improvements in training efficiency and more than 2times faster sampling within the low-variance regime without degrading sample quality. Our code is available at https://github.com/linYDTHU/StableVelocity.

We propose a modified moment matching algorithm to avoid catastrophic failures for sources with a low signal to noise ratio (SNR). The proposed modifications include a method to eliminate non-physical negative pixel values and a forced single iteration with an initial guess derived from co-add measurements when iterative methods are unstable. We correct for all biases in measurements introduced by the method. We find that the proposed modifications allow the algorithm to avoid catastrophic failures in nearly 100\% of the cases, especially at low signal to noise ratio. Additionally, with a reasonable guess from co-add measurements, the algorithm measures the flux, centroid, size, shape and ellipticity with bias statistically consistent with zero. We show the proposed method allows us to measure sources seven times fainter than traditional methods when applied to images obtained from WIYN-ODI. We also present a scheme to find uncertainties in measurements when using the new method to measure astronomical sources.

Flow matching has emerged as a compelling generative modeling approach that is widely used across domains. To generate data via a flow matching model, an ordinary differential equation (ODE) is numerically solved via forward integration of the modeled velocity field. To better capture the multi-modality that is inherent in typical velocity fields, hierarchical flow matching was recently introduced. It uses a hierarchy of ODEs that are numerically integrated when generating data. This hierarchy of ODEs captures the multi-modal velocity distribution just like vanilla flow matching is capable of modeling a multi-modal data distribution. While this hierarchy enables to model multi-modal velocity distributions, the complexity of the modeled distribution remains identical across levels of the hierarchy. In this paper, we study how to gradually adjust the complexity of the distributions across different levels of the hierarchy via mini-batch couplings. We show the benefits of mini-batch couplings in hierarchical rectified flow matching via compelling results on synthetic and imaging data. Code is available at https://riccizz.github.io/HRF_coupling.

Flow Matching (FM) constructs linear conditional probability paths, but the learned marginal velocity field inevitably exhibits strong curvature due to trajectory superposition. This curvature severely inflates numerical truncation errors, bottlenecking few-step sampling. To overcome this, we introduce Isokinetic Flow Matching (Iso-FM), a lightweight, Jacobian-free dynamical regularizer that directly penalizes pathwise acceleration. By using a self-guided finite-difference approximation of the material derivative Dv/Dt, Iso-FM enforces local velocity consistency without requiring auxiliary encoders or expensive second-order autodifferentiation. Operating as a pure plug-and-play addition to single-stage FM training, Iso-FM dramatically improves few-step generation. On CIFAR-10 (DiT-S/2), Iso-FM slashes conditional non-OT FID at 2 steps from 78.82 to 27.13 - a 2.9x relative efficiency gain - and reaches a best-observed FID at 4 steps of 10.23. These results firmly establish acceleration regularization as a principled, compute-efficient mechanism for fast generative sampling.

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

Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy; for exact displacement interpolation, the associated Lagrangian particle dynamics are integrated exactly by Euler. Motivated by this analysis, we study weighted Jacobian regularization with strain weight alpha and vorticity weight beta. Experiments on 2D synthetic data confirm the main theoretical predictions, showing up to 2.7x lower integration error at NFE=5. Preliminary CIFAR-10 experiments show consistent trends, with a lightweight fine-tuning procedure improving FID by 14 percent at NFE=10 while preserving high-NFE quality.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

Diffusion models and Flow Matching generate high-quality samples but are slow at inference, and distilling them into few-step models often leads to instability and extensive tuning. To resolve these trade-offs, we propose Inductive Moment Matching (IMM), a new class of generative models for one- or few-step sampling with a single-stage training procedure. Unlike distillation, IMM does not require pre-training initialization and optimization of two networks; and unlike Consistency Models, IMM guarantees distribution-level convergence and remains stable under various hyperparameters and standard model architectures. IMM surpasses diffusion models on ImageNet-256x256 with 1.99 FID using only 8 inference steps and achieves state-of-the-art 2-step FID of 1.98 on CIFAR-10 for a model trained from scratch.

Video moment retrieval (VMR) identifies a specific moment in an untrimmed video for a given natural language query. This task is prone to suffer the weak alignment problem innate in video datasets. Due to the ambiguity, a query does not fully cover the relevant details of the corresponding moment, or the moment may contain misaligned and irrelevant frames, potentially limiting further performance gains. To tackle this problem, we propose a background-aware moment detection transformer (BM-DETR). Our model adopts a contrastive approach, carefully utilizing the negative queries matched to other moments in the video. Specifically, our model learns to predict the target moment from the joint probability of each frame given the positive query and the complement of negative queries. This leads to effective use of the surrounding background, improving moment sensitivity and enhancing overall alignments in videos. Extensive experiments on four benchmarks demonstrate the effectiveness of our approach. Our code is available at: https://github.com/minjoong507/BM-DETR

Flow matching policies learn continuous velocity fields that transport noise to actions, enabling fast deterministic inference for robot manipulation. However, standard training optimizes a pointwise velocity objective while inference requires numerical integration of that field -- a mismatch that causes compounding trajectory errors. We propose four complementary remedies: (1) auxiliary rectified flow velocity regression that provides uniform temporal supervision across the full time interval; (2) multi-step trajectory consistency training that supervises the integrated displacement of the velocity field over trajectory segments, directly closing the train-inference gap; (3) velocity field regularization that enforces temporal smoothness, preventing oscillations that destabilize integration; and (4) fourth-order Runge-Kutta (RK4) inference that reduces global discretization error by orders of magnitude over Euler methods. Critically, these components are not independently sufficient -- RK4 without a smooth velocity field fails, and smoothness without trajectory-level supervision still drifts, as our ablation study confirms. We further pair these with a dual-view 3D point cloud encoder using two independent PointNet encoders for complementary spatial perception. On four real-robot tasks across a Franka arm and a Boston Dynamics Spot, our method achieves 70% and 60% overall success on two long-horizon multi-phase tasks where both baselines score 0%, and reaches 100% on precision tool placement. Three MetaWorld simulation tasks confirm consistent improvements, validating that trajectory-level supervision is essential for reliable policy execution.

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

Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into a straight line for a few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of flow matching is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned v-prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, FID = 10.05).

Tagged magnetic resonance imaging (tMRI) has been employed for decades to measure the motion of tissue undergoing deformation. However, registration-based motion estimation from tMRI is difficult due to the periodic patterns in these images, particularly when the motion is large. With a larger motion the registration approach gets trapped in a local optima, leading to motion estimation errors. We introduce a novel "momenta, shooting, and correction" framework for Lagrangian motion estimation in the presence of repetitive patterns and large motion. This framework, grounded in Lie algebra and Lie group principles, accumulates momenta in the tangent vector space and employs exponential mapping in the diffeomorphic space for rapid approximation towards true optima, circumventing local optima. A subsequent correction step ensures convergence to true optima. The results on a 2D synthetic dataset and a real 3D tMRI dataset demonstrate our method's efficiency in estimating accurate, dense, and diffeomorphic 2D/3D motion fields amidst large motion and repetitive patterns.

Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead in inference, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging tasks of high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards the conditional velocity field. However, on constrained domains, the learned velocity model may lead to undesirable flows that result in highly unnatural samples, e.g., oversaturated images, due to both flow matching error and simulation error. To address this, we add a boundary constraint term to CNFs, which leads to reflected CNFs that keep trajectories within the constrained domains. We propose reflected flow matching (RFM) to train the velocity model in reflected CNFs by matching the conditional velocity fields in a simulation-free manner, similar to the vanilla FM. Moreover, the analytical form of conditional velocity fields in RFM avoids potentially biased approximations, making it superior to existing score-based generative models on constrained domains. We demonstrate that RFM achieves comparable or better results on standard image benchmarks and produces high-quality class-conditioned samples under high guidance weight.

Event-based cameras are ideal for line-based motion estimation, since they predominantly respond to edges in the scene. However, accurately determining the camera displacement based on events continues to be an open problem. This is because line feature extraction and dynamics estimation are tightly coupled when using event cameras, and no precise model is currently available for describing the complex structures generated by lines in the space-time volume of events. We solve this problem by deriving the correct non-linear parametrization of such manifolds, which we term eventails, and demonstrate its application to event-based linear motion estimation, with known rotation from an Inertial Measurement Unit. Using this parametrization, we introduce a novel minimal 5-point solver that jointly estimates line parameters and linear camera velocity projections, which can be fused into a single, averaged linear velocity when considering multiple lines. We demonstrate on both synthetic and real data that our solver generates more stable relative motion estimates than other methods while capturing more inliers than clustering based on spatio-temporal planes. In particular, our method consistently achieves a 100% success rate in estimating linear velocity where existing closed-form solvers only achieve between 23% and 70%. The proposed eventails contribute to a better understanding of spatio-temporal event-generated geometries and we thus believe it will become a core building block of future event-based motion estimation algorithms.

Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal dynamics, as real-world sequences often exhibit random fluctuations and localized variations. While diffusion models have achieved remarkable success, their generation process is computationally inefficient, often requiring hundreds to thousands of expensive function evaluations per sample. Flow matching has emerged as a more efficient paradigm, yet its conventional ordinary differential equation (ODE)-based formulation fails to explicitly capture stochasticity, thereby limiting the fidelity of generated sequences. By contrast, stochastic differential equation (SDE) are naturally suited for modeling randomness and uncertainty. Motivated by these insights, we propose TimeFlow, a novel SDE-based flow matching framework that integrates a encoder-only architecture. Specifically, we design a component-wise decomposed velocity field to capture the multi-faceted structure of time series and augment the vanilla flow-matching optimization with an additional stochastic term to enhance representational expressiveness. TimeFlow is flexible and general, supporting both unconditional and conditional generation tasks within a unified framework. Extensive experiments across diverse datasets demonstrate that our model consistently outperforms strong baselines in generation quality, diversity, and efficiency.

Video Moment Retrieval (VMR) aims to localize temporal segments in videos that correspond to a natural language query, but typically assumes only a single matching moment for each query. This assumption does not always hold in real-world scenarios, where queries may correspond to multiple or no moments. Thus, we formulate Generalized Moment Retrieval (GMR), a unified setting that requires retrieving the complete set of relevant moments or predicting an empty set. To enable systematic study of GMR, we introduce Soccer-GMR, a large-scale benchmark built on challenging soccer videos that reflect general GMR scenarios, with realistic negative and positive queries. The benchmark is constructed via a duration-flexible semi-automated pipeline with human verification, enabling scalable data generation while maintaining high annotation quality. We further design a unified evaluation protocol with complementary metrics tailored for null-set rejection, positive-query localization, and end-to-end GMR performance. Finally, we establish strong baselines across two modeling paradigms: a lightweight plug-and-play GMR adapter for discriminative VMR models, and a GMR-tailored GRPO reward for fine-tuning multimodal large language models (MLLMs). Extensive experiments show consistent gains across all metrics and expose key limitations of current methods, positioning GMR as a more realistic and challenging benchmark for video-language understanding.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a regularized mirror map that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-t prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-t priors and primal-space guarantees for constrained generation, under varepsilon-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.

Flow matching has recently emerged as a strong paradigm for state-of-the-art text-to-image (T2I) generation, enabling high-quality generation with a small number of sampling steps. As these models are increasingly integrated into real-world applications, ensuring safe and non-sensitive content generation has become a critical requirement. However, adapting safety and concept removal methods to this new generation framework remains an open challenge. Specifically, prior methods largely rely on iterative trajectory steering across a number of denoising steps or on CLIP-centric prompt embedding manipulation. These design assumptions pose fundamental bottlenecks for safety in flow matching-based T2I generation, where limited sampling steps constrain iterative correction and modern context-aware text encoders diminish the effectiveness of embedding-level interventions. In this paper, we propose VESFlow, a training-free safety method tailored to flow matching with extremely few sampling steps. Leveraging the fact that flow matching models learn the marginal velocity, we directly edit the velocity field via a safe-conditional posterior. VESFlow steers the trajectory toward safe outputs while leaving the conditioning prompt unchanged. Building on the observation that VESFlow leaves outputs unchanged under benign prompts, we further introduce a risk score-based filtering that bypasses velocity editing to reduce computational cost while preserving benign prompt generation. Based on this filtering, we propose VESFlow+, a stronger variant of VESFlow that not only edits the velocity toward the safe direction, but also pushes it away from the unsafe direction. Experimental results show that VESFlow+ removes the target concept, reducing the attack success rate by NudeNet to 6.3% on Ring-A-Bell and 6.8% on MMA-Diffusion on the 4-step MeanFlow model, while preserving fidelity on benign prompts.

We propose amortized moment matching, utilizing neural networks to learn data moments as distributional training signals. By casting diffusion denoisers through polynomial projections, we establish a general framework for moment amortization, revealing that an n-th degree projection explicitly identifies data moments up to order n+1. Derived from the tractable affine case, we instantiate the Amortized Fréchet Distance (AMFD) loss. Unlike FD-loss which relies on explicit marginal moment calculations, AMFD is able to dynamically learn conditional moments via an alternating, matrix-free optimization pipeline that effortlessly scales to high-dimensional data. When operating on global representation features, AMFD serves as a powerful post-training objective; empirically, its neural formulation yields more robust training dynamics than exact statistical matching, substantially surpassing the FD baseline on the FDr^6 metric and achieving superior one-step generation on ImageNet. Furthermore, it unlocks direct exploration within native generative spaces, suggesting that the first two moments can identify target distributions only in spaces with strong semantics. Finally, when scaled to text-to-image generation, the condition-aware nature of AMFD unlocks massive gains in instruction-following capabilities, enabling our one-step models to outperform their multi-step FLUX.2 [klein] 4B teachers on the GenEval benchmark while achieving on-par performance on PickScore. Code and checkpoints are available at https://github.com/poppuppy/amfd.

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

Flow matching approaches to imaging inverse problems commonly incorporate measurements in two ways. Conditioning-based approaches supply measurement-derived information as a network input, often through concatenation, while inference-guided approaches combine an unconditional velocity field with a separate data-consistency update. In these common formulations, the forward model is not explicitly enforced within the learned conditional velocity field. We propose a principled parametrization of the measurement-conditional velocity field to solve inverse problems. Under linear interpolation, we express the conditional velocity v(x_t,t,y) in terms of the posterior mean E[x_1 | x_t,y], and characterize that mean as the unique minimizer of a variational objective whose data-consistency term is explicit. We further prove that the velocity field defines a probability flow from the source distribution to the measurement-conditioned posterior. Splitting the variational objective yields a conditional velocity parameterization with operator-dependent data-consistency updates, which we train end-to-end under the flow-matching objective, with no additional guidance at inference. Our method achieves state-of-the-art PSNR with 50times fewer function evaluations than the strongest flow baseline. Varying the sampling steps provides test-time control over the distortion-perception trade-off without retraining.

Flow Matching (FM) has recently emerged as a principled and efficient alternative to diffusion models. Standard FM encourages the learned velocity field to follow a target direction; however, it may accumulate errors along the trajectory and drive samples off the data manifold, leading to perceptual degradation, especially in lightweight or low-step configurations. To enhance stability and generalization, we extend FM into a balanced attract-repel scheme that provides explicit guidance on both "where to go" and "where not to go." To be formal, we propose Velocity Contrastive Regularization (VeCoR), a complementary training scheme for flow-based generative modeling that augments the standard FM objective with contrastive, two-sided supervision. VeCoR not only aligns the predicted velocity with a stable reference direction (positive supervision) but also pushes it away from inconsistent, off-manifold directions (negative supervision). This contrastive formulation transforms FM from a purely attractive, one-sided objective into a two-sided training signal, regularizing trajectory evolution and improving perceptual fidelity across datasets and backbones. On ImageNet-1K 256times256, VeCoR yields 22\% and 35\% relative FID reductions on SiT-XL/2 and REPA-SiT-XL/2 backbones, respectively, and achieves further FID gains (32\% relative) on MS-COCO text-to-image generation, demonstrating consistent improvements in stability, convergence, and image quality, particularly in low-step and lightweight settings. Project page: https://p458732.github.io/VeCoR_Project_Page/

Video Moment Retrieval (VMR) is a task to localize the temporal moment in untrimmed video specified by natural language query. For VMR, several methods that require full supervision for training have been proposed. Unfortunately, acquiring a large number of training videos with labeled temporal boundaries for each query is a labor-intensive process. This paper explores methods for performing VMR in a weakly-supervised manner (wVMR): training is performed without temporal moment labels but only with the text query that describes a segment of the video. Existing methods on wVMR generate multi-scale proposals and apply query-guided attention mechanisms to highlight the most relevant proposal. To leverage the weak supervision, contrastive learning is used which predicts higher scores for the correct video-query pairs than for the incorrect pairs. It has been observed that a large number of candidate proposals, coarse query representation, and one-way attention mechanism lead to blurry attention maps which limit the localization performance. To handle this issue, Video-Language Alignment Network (VLANet) is proposed that learns sharper attention by pruning out spurious candidate proposals and applying a multi-directional attention mechanism with fine-grained query representation. The Surrogate Proposal Selection module selects a proposal based on the proximity to the query in the joint embedding space, and thus substantially reduces candidate proposals which leads to lower computation load and sharper attention. Next, the Cascaded Cross-modal Attention module considers dense feature interactions and multi-directional attention flow to learn the multi-modal alignment. VLANet is trained end-to-end using contrastive loss which enforces semantically similar videos and queries to gather. The experiments show that the method achieves state-of-the-art performance on Charades-STA and DiDeMo datasets.

We propose Terminal Velocity Matching (TVM), a generalization of flow matching that enables high-fidelity one- and few-step generative modeling. TVM models the transition between any two diffusion timesteps and regularizes its behavior at its terminal time rather than at the initial time. We prove that TVM provides an upper bound on the 2-Wasserstein distance between data and model distributions when the model is Lipschitz continuous. However, since Diffusion Transformers lack this property, we introduce minimal architectural changes that achieve stable, single-stage training. To make TVM efficient in practice, we develop a fused attention kernel that supports backward passes on Jacobian-Vector Products, which scale well with transformer architectures. On ImageNet-256x256, TVM achieves 3.29 FID with a single function evaluation (NFE) and 1.99 FID with 4 NFEs. It similarly achieves 4.32 1-NFE FID and 2.94 4-NFE FID on ImageNet-512x512, representing state-of-the-art performance for one/few-step models from scratch.

Flow matching (FM) has become a popular action head paradigm for modern embodied models. However, as a conditional generative model, it does not explicitly expose its inherent uncertainty, producing faulty action chunks even when it misinterprets the scene or encounters out-of-distribution (OOD) inputs. Therefore, determining when an FM-generated action can be trusted is essential for safe deployment, yet existing uncertainty estimation methods on real-time control suffer from several issues: extra training budget, high computational overhead, and low generalization ability. In this work, we provide a geometric interpretation of FM uncertainty in the velocity field, showing that uncertainty manifests as deviation from an ideal affine-isotropic contraction field. Building on this observation, we introduce denoising acceleration (accel), a highly-generalizable and cost-free uncertainty proxy that measures the bending of the denoising trajectory from a single forward pass, without additional model evaluations, training, or resampling. We theoretically and empirically demonstrate that accel is a faithful proxy for FM uncertainty and further test its utility in online failure detection. Results show that accel identifies failing rollouts well before termination, matching or even outperforming costly resampling- and training-based baselines across settings under realistic deployment budget. Code and demos available at: https://github.com/rrrrrrzy/fm-geometry.

In this paper, we propose the task of Ranked Video Moment Retrieval (RVMR) to locate a ranked list of matching moments from a collection of videos, through queries in natural language. Although a few related tasks have been proposed and studied by CV, NLP, and IR communities, RVMR is the task that best reflects the practical setting of moment search. To facilitate research in RVMR, we develop the TVR-Ranking dataset, based on the raw videos and existing moment annotations provided in the TVR dataset. Our key contribution is the manual annotation of relevance levels for 94,442 query-moment pairs. We then develop the NDCG@K, IoUgeq mu evaluation metric for this new task and conduct experiments to evaluate three baseline models. Our experiments show that the new RVMR task brings new challenges to existing models and we believe this new dataset contributes to the research on multi-modality search. The dataset is available at https://github.com/Ranking-VMR/TVR-Ranking

Existing Video Corpus Moment Retrieval (VCMR) is limited to coarse-grained understanding, which hinders precise video moment localization when given fine-grained queries. In this paper, we propose a more challenging fine-grained VCMR benchmark requiring methods to localize the best-matched moment from the corpus with other partially matched candidates. To improve the dataset construction efficiency and guarantee high-quality data annotations, we propose VERIFIED, an automatic VidEo-text annotation pipeline to generate captions with RelIable FInE-grained statics and Dynamics. Specifically, we resort to large language models (LLM) and large multimodal models (LMM) with our proposed Statics and Dynamics Enhanced Captioning modules to generate diverse fine-grained captions for each video. To filter out the inaccurate annotations caused by the LLM hallucination, we propose a Fine-Granularity Aware Noise Evaluator where we fine-tune a video foundation model with disturbed hard-negatives augmented contrastive and matching losses. With VERIFIED, we construct a more challenging fine-grained VCMR benchmark containing Charades-FIG, DiDeMo-FIG, and ActivityNet-FIG which demonstrate a high level of annotation quality. We evaluate several state-of-the-art VCMR models on the proposed dataset, revealing that there is still significant scope for fine-grained video understanding in VCMR. Code and Datasets are in https://github.com/hlchen23/VERIFIED{https://github.com/hlchen23/VERIFIED}.

Monocular 3D pose estimation is fundamentally ill-posed due to depth ambiguity and occlusions, thereby motivating probabilistic methods that generate multiple plausible 3D pose hypotheses. In particular, diffusion-based models have recently demonstrated strong performance, but their iterative denoising process typically requires many timesteps for each prediction, making inference computationally expensive. In contrast, we leverage Flow Matching (FM) to learn a velocity field defined by an Ordinary Differential Equation (ODE), enabling efficient generation of 3D pose samples with only a few integration steps. We propose a novel generative pose estimation framework, FMPose3D, that formulates 3D pose estimation as a conditional distribution transport problem. It continuously transports samples from a standard Gaussian prior to the distribution of plausible 3D poses conditioned only on 2D inputs. Although ODE trajectories are deterministic, FMPose3D naturally generates various pose hypotheses by sampling different noise seeds. To obtain a single accurate prediction from those hypotheses, we further introduce a Reprojection-based Posterior Expectation Aggregation (RPEA) module, which approximates the Bayesian posterior expectation over 3D hypotheses. FMPose3D surpasses existing methods on the widely used human pose estimation benchmarks Human3.6M and MPI-INF-3DHP, and further achieves state-of-the-art performance on the 3D animal pose datasets Animal3D and CtrlAni3D, demonstrating strong performance across both 3D pose domains. The code is available at https://github.com/AdaptiveMotorControlLab/FMPose3D.

Recent years have seen significant advancements in foundation models through generative pre-training, yet algorithmic innovation in this space has largely stagnated around autoregressive models for discrete signals and diffusion models for continuous signals. This stagnation creates a bottleneck that prevents us from fully unlocking the potential of rich multi-modal data, which in turn limits the progress on multimodal intelligence. We argue that an inference-first perspective, which prioritizes scaling efficiency during inference time across sequence length and refinement steps, can inspire novel generative pre-training algorithms. Using Inductive Moment Matching (IMM) as a concrete example, we demonstrate how addressing limitations in diffusion models' inference process through targeted modifications yields a stable, single-stage algorithm that achieves superior sample quality with over an order of magnitude greater inference efficiency.

Flow matching with clean-data prediction has shown that regressing the clean point can exploit low-dimensional structure more effectively than predicting an ambient noised quantity. We ask whether this principle remains useful after images are mapped into a learned latent space, where compression has already removed much of the raw pixel variability. We introduce JLT, a 130M latent diffusion Transformer over frozen FLUX.2 VAE codes, and compare clean-latent prediction with a matched velocity-prediction DiT under the same representation, backbone, and training settings. Although the three variables x, epsilon, and v are linearly convertible for a fixed corruption time, a local Gaussian analysis shows that velocity regression inherits an isotropic target-covariance floor and amplifies low-variance latent directions, while clean prediction damps them. On ImageNet 256 x 256, JLT-B/1 obtains FID-50K 2.50 with classifier-free guidance, with a large matched-target gap over velocity prediction. These results suggest that prediction targets in latent diffusion are representation-dependent geometric choices, rather than interchangeable algebraic parameterizations.

Classifier-free guidance (CFG) is a widely used technique for controllable generation in diffusion and flow-based models. Despite its empirical success, CFG relies on a heuristic linear extrapolation that is often sensitive to the guidance scale. In this work, we provide a principled interpretation of CFG through the lens of optimization. We demonstrate that the velocity field in flow matching corresponds to the gradient of a sequence of smoothed distance functions, which guides latent variables toward the scaled target image set. This perspective reveals that the standard CFG formulation is an approximation of this gradient, where the prediction gap, the discrepancy between conditional and unconditional outputs, governs guidance sensitivity. Leveraging this insight, we reformulate the CFG sampling as a homotopy optimization with a manifold constraint. This formulation necessitates a manifold projection step, which we implement via an incremental gradient descent scheme during sampling. To improve computational efficiency and stability, we further enhance this iterative process with Anderson Acceleration without requiring additional model evaluations. Our proposed methods are training-free and consistently refine generation fidelity, prompt alignment, and robustness to the guidance scale. We validate their effectiveness across diverse benchmarks, demonstrating significant improvements on large-scale models such as DiT-XL-2-256, Flux, and Stable Diffusion 3.5.

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems show that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

Counterfactual generation seeks to sample outcomes under a hypothetical intervention or decision using observational data collected under the factual assignment mechanism. We develop a flow-matching approach that combines a sample-split, doubly robust training objective with a learned coupling between observed source outcomes and target outcomes drawn from a fitted conditional outcome model. To enable finite-step generation, we leverage a score-corrected stochastic sampler based on a Gaussian-smoothed interpolation. Our main theoretical contribution is a coupling-sensitive KL bound for constant-step Euler discretization: the error is controlled by moments of the source--target displacement under the chosen coupling, rather than by global uniform regularity of the velocity field, and has near-linear dependence on the ambient dimension. We also establish finite-sample non-parametric guarantees for the learned velocity and score fields when both the conditional outcome model and the source-target coupling are estimated from data. These bounds separate approximation, coupling-replacement, nuisance-estimation, generalization, and Monte Carlo errors and, combined with the sampler analysis, yield an end-to-end guarantee for counterfactual generation. Experiments on synthetic and semi-synthetic image benchmarks support the coupling-dependent theory and show that, at finite discretization budgets, the stochastic sampler can outperform the corresponding deterministic ODE sampler.

Flow-matching models generate samples through iterative velocity predictions, but typically do not revisit these predictions using the intermediate representations that produced them. We introduce CorrFlow, a self-correcting flow-matching framework that reuses this information through a lightweight refiner. Under rectified-flow interpolation, the error of the one-step clean prediction equals the realized velocity residual scaled by the noise level. Motivated by this identity, the refiner learns to predict residual corrections from the base model's clean prediction, conditioning, noise level and hidden states from the same forward pass. The correction is added to the base velocity before each sampling update, so subsequent predictions are made from the corrected state. This requires no additional base-model evaluations and only one lightweight refiner evaluation per step. Our theoretical analyses establish conditions under which feature reuse outperforms raw-input affine predictors and refiner training achieves greater residual-risk reduction than continued base-model training under a matched training compute budget. Experiments on class-conditional image generation, text-to-video generation and image-to-video generation show consistent improvements over the corresponding base models, including gains in visual quality and physical consistency. Project Page: https://fogradio.github.io/corrflow-project

Representation Autoencoders (RAEs) enable diffusion models to operate in the feature spaces of pretrained visual encoders. However, many off-the-shelf encoders are not optimized for faithful reconstruction, discarding fine-grained visual details. As expected, finetuning these encoders for image reconstruction recovers such details. However, perhaps counterintuitively, this procedure reduces the effective dimensionality of the resulting representation, and the altered geometry has downstream effects on generation. Specifically, we show that using the standard velocity prediction in flow matching in this high-dimensional space requires the model to fit orthogonal noise directions outside the low-dimensional signal manifold, making optimization inefficient. This motivates using the clean data parameterization (x_{0}-prediction) instead, which focuses learning on the underlying signal manifold. Across experiments with multiple strong-reconstruction encoders, we show that x_{0}-prediction consistently improves text-to-image generation performance.

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

Data-driven MoCap-to-radar models generate plausible micro-Doppler spectrograms, but do they actually learn the underlying physics? We introduce a physics-based interpretability framework to answer this question via two proposed complementary metrics: one measures alignment between model predictions and the physics-derived Doppler frequency, while the other tests whether predictions preserve the velocity-frequency relationship under velocity intervention. Both metrics require only MoCap input and model predictions, without access to measured radar data. Experiments across several model architectures reveal that low reconstruction error does not guarantee physical consistency: some, but not all, models achieve low error yet perform poorly on the two physics-based metrics. Further analysis shows that temporal attention is critical for transformer-based models to learn the underlying physics.

Many Multi-Object Tracking (MOT) approaches exploit motion information to associate all the detected objects across frames. However, many methods that rely on filtering-based algorithms, such as the Kalman Filter, often work well in linear motion scenarios but struggle to accurately predict the locations of objects undergoing complex and non-linear movements. To tackle these scenarios, we propose a motion-based MOT approach with an enhanced temporal motion predictor, ETTrack. Specifically, the motion predictor integrates a transformer model and a Temporal Convolutional Network (TCN) to capture short-term and long-term motion patterns, and it predicts the future motion of individual objects based on the historical motion information. Additionally, we propose a novel Momentum Correction Loss function that provides additional information regarding the motion direction of objects during training. This allows the motion predictor rapidly adapt to motion variations and more accurately predict future motion. Our experimental results demonstrate that ETTrack achieves a competitive performance compared with state-of-the-art trackers on DanceTrack and SportsMOT, scoring 56.4% and 74.4% in HOTA metrics, respectively.

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject

Latent diffusion models leverage visual tokenizers to compress images into latent spaces for efficient generative modeling. However, better reconstruction quality of a tokenizer does not necessarily translate into better generation quality, suggesting that latent representations should be evaluated not only by fidelity but also by their diffusability. Recent studies have proposed diverse explanations for diffusion-friendly latent spaces, including semantic separability, affine equivariance, distribution uniformity, spatial structure, spectral smoothness, and manifold continuity. Yet these properties are often validated on a limited set of tokenizers, leaving it unclear which factors are most predictive of downstream generation quality and whether such conclusions hold beyond the specific settings in which they are introduced. In this work, we conduct a systematic study of latent diffusability by training a large collection of tokenizers with diverse regularization strategies, architectures, and latent configurations, and evaluating them with multiple downstream diffusion backbones. Our analysis identifies several latent properties that consistently correlate with generation quality and exhibit strong generalization across experimental settings. Beyond existing metrics, we introduce Velocity Irreducible Variance (VIV), a measure of velocity ambiguity induced by trajectory crossings. Extensive experiments show that VIV is one of the most stable predictors of generation quality.

Earthquake hazard analysis and design of spatially distributed infrastructure, such as power grids and energy pipeline networks, require scenario-specific ground-motion time histories with realistic frequency content and spatiotemporal coherence. However, producing the large ensembles needed for uncertainty quantification with physics-based simulations is computationally intensive and impractical for engineering workflows. To address this challenge, we introduce Ground-Motion Flow (GMFlow), a physics-inspired latent operator flow matching framework that generates realistic, large-scale regional ground-motion time-histories conditioned on physical parameters. Validated on simulated earthquake scenarios in the San Francisco Bay Area, GMFlow generates spatially coherent ground motion across more than 9 million grid points in seconds, achieving a 10,000-fold speedup over the simulation workflow, which opens a path toward rapid and uncertainty-aware hazard assessment for distributed infrastructure. More broadly, GMFlow advances mesh-agnostic functional generative modeling and could potentially be extended to the synthesis of large-scale spatiotemporal physical fields in diverse scientific domains.

MeanFlow generators achieve fast few-step sampling by predicting average velocities over time intervals, making them attractive for efficient generation. Reinforcement learning (RL) has become a powerful way to align diffusion and flow models with human preferences and task-specific objectives. In particular, DiffusionNFT offers an efficient forward-process RL framework that does not require reverse-process trajectories or likelihood estimation. However, applying such RL methods to MeanFlow remains underexplored. DiffusionNFT optimizes instantaneous velocities, whereas MeanFlow samples with average velocities. To bridge this gap, we introduce MeanFlowNFT. Inspired by the MeanFlow identity, which bridges average and instantaneous velocities, we construct an induced instantaneous-velocity predictor. We apply the DiffusionNFT objective to this predictor, making reward optimization well-defined for MeanFlow. Sampling remains based on the average velocity, preserving MeanFlow's fast few-step generation. We further prove that MeanFlowNFT inherits DiffusionNFT's strict policy-improvement guarantee. Experiments on image and video generation show that MeanFlowNFT consistently improves baselines. Moreover, it outperforms prior state-of-the-art RL-tuned few-step generators on most metrics (6 of 8 on SD3.5-M), and can even surpass multi-step RL-tuned diffusion while using only a few sampling steps. For instance, on Wan 2.1, 4-step MeanFlowNFT reaches a VBench score of 84.33, surpassing 50-step LongCat-Video RL (82.57).

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules -- such as GANs or reward models -- to restore visual fidelity. In this work, we introduce Continuous-Time Distribution Matching (CDM), migrating the DMD framework from discrete anchoring to continuous optimization for the first time. CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives. Code is available at https://github.com/byliutao/cdm.

Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator variance and inefficient sampling. Prior approaches mitigate this via explicit smoothness penalties, trajectory regularization, or modified probability paths and solvers. We introduce Temporal Pair Consistency (TPC), a lightweight variance-reduction principle that couples velocity predictions at paired timesteps along the same probability path, operating entirely at the estimator level without modifying the model architecture, probability path, or solver. We provide a theoretical analysis showing that TPC induces a quadratic, trajectory-coupled regularization that provably reduces gradient variance while preserving the underlying flow-matching objective. Instantiated within flow matching, TPC improves sample quality and efficiency across CIFAR-10 and ImageNet at multiple resolutions, achieving lower FID at identical or lower computational cost than prior methods, and extends seamlessly to modern SOTA-style pipelines with noise-augmented training, score-based denoising, and rectified flow.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.

Pixel-space generative models bypass lossy latent compression, yet necessitate joint learning of global structure and fine-grained details in a high-dimensional space. Standard flow matching interpolates noise toward a fixed clean-image endpoint, leaving the spectral evolution to be learned implicitly. In this paper, we introduce Energy-Guided Flow Matching(EG-FM) that explicitly models a coarse-to-fine generative trajectory by moving endpoint. Specifically, EG-FM replaces the fixed endpoint with a heat-kernel-filtered endpoint that evolves smoothly from low-frequency image to clean image. The fraction of high-frequency signal in moving endpoint is released by an image-specific energy-guided scheduling, leading to the re-targeting of velocity in flow matching. Our framework requires no adaptation of the backbone and training data, bringing negligible cost on the training and inference stages. In our experiment, EG-FM consistently achieves lower FID on the ImageNet class-conditional image generation task at 256 times 256 with fewer epochs, reaching an FID of 1.55 at 200 epochs and 1.45 at 600 epochs. We continue training the generation task on the setting of 512 times 512 resolution, yielding a FID of 1.58 after only 40 high-resolution adaptation epochs. Furthermore, we transfer EG-FM on text-to-image generation and achieve 0.85 on GenEval score and 83.9 on DPG-Bench. Code is available at https://github.com/ysng123/EG-FM.

We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, in contrast with previous approaches. The new estimator makes covariance estimation tractable in applications where simulation or data collection is expensive; to that end, we develop an optimal sample allocation scheme that minimizes the mean-squared error of the estimator given a fixed budget. Guaranteed definiteness is crucial to metric learning, data assimilation, and other downstream tasks. Evaluations of our approach using data from physical applications (heat conduction, fluid dynamics) demonstrate more accurate metric learning and speedups of more than one order of magnitude compared to benchmarks.

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite their effectiveness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, we propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations. Additionally, we propose a lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost. Extensive experiments on ImageNet 256x256 demonstrate that BFM establishes a substantially improved Pareto frontier over existing Flow Matching methods, achieving 2.1x to 4.9x accelerations in inference complexity at comparable generation performance. Code is available at https://github.com/mlvlab/BFM.

Human motion capture from monocular videos has made significant progress in recent years. However, modern approaches often produce temporal artifacts, e.g. in form of jittery motion and struggle to achieve smooth and physically plausible motions. Explicitly integrating physics, in form of internal forces and exterior torques, helps alleviating these artifacts. Current state-of-the-art approaches make use of an automatic PD controller to predict torques and reaction forces in order to re-simulate the input kinematics, i.e. the joint angles of a predefined skeleton. However, due to imperfect physical models, these methods often require simplifying assumptions and extensive preprocessing of the input kinematics to achieve good performance. To this end, we propose a novel method to selectively incorporate the physics models with the kinematics observations in an online setting, inspired by a neural Kalman-filtering approach. We develop a control loop as a meta-PD controller to predict internal joint torques and external reaction forces, followed by a physics-based motion simulation. A recurrent neural network is introduced to realize a Kalman filter that attentively balances the kinematics input and simulated motion, resulting in an optimal-state dynamics prediction. We show that this filtering step is crucial to provide an online supervision that helps balancing the shortcoming of the respective input motions, thus being important for not only capturing accurate global motion trajectories but also producing physically plausible human poses. The proposed approach excels in the physics-based human pose estimation task and demonstrates the physical plausibility of the predictive dynamics, compared to state of the art. The code is available on https://github.com/cuongle1206/OSDCap

In this paper, we present TMR, a simple yet effective approach for text to 3D human motion retrieval. While previous work has only treated retrieval as a proxy evaluation metric, we tackle it as a standalone task. Our method extends the state-of-the-art text-to-motion synthesis model TEMOS, and incorporates a contrastive loss to better structure the cross-modal latent space. We show that maintaining the motion generation loss, along with the contrastive training, is crucial to obtain good performance. We introduce a benchmark for evaluation and provide an in-depth analysis by reporting results on several protocols. Our extensive experiments on the KIT-ML and HumanML3D datasets show that TMR outperforms the prior work by a significant margin, for example reducing the median rank from 54 to 19. Finally, we showcase the potential of our approach on moment retrieval. Our code and models are publicly available at https://mathis.petrovich.fr/tmr.

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

The moments (a.k.a., mean and standard deviation) of latent features are often removed as noise when training image recognition models, to increase stability and reduce training time. However, in the field of image generation, the moments play a much more central role. Studies have shown that the moments extracted from instance normalization and positional normalization can roughly capture style and shape information of an image. Instead of being discarded, these moments are instrumental to the generation process. In this paper we propose Moment Exchange, an implicit data augmentation method that encourages the model to utilize the moment information also for recognition models. Specifically, we replace the moments of the learned features of one training image by those of another, and also interpolate the target labels -- forcing the model to extract training signal from the moments in addition to the normalized features. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation approaches. We demonstrate its efficacy across several recognition benchmark data sets where it improves the generalization capability of highly competitive baseline networks with remarkable consistency.

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

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

3D reconstruction in dynamic scenes primarily relies on the combination of geometry estimation and matching modules where the latter task is pivotal for distinguishing dynamic regions which can help to mitigate the interference introduced by camera and object motion. Furthermore, the matching module explicitly models object motion, enabling the tracking of specific targets and advancing motion understanding in complex scenarios. Recently, the proposed representation of pointmap in DUSt3R suggests a potential solution to unify both geometry estimation and matching in 3D space, but it still struggles with ambiguous matching in dynamic regions, which may hamper further improvement. In this work, we present POMATO, a unified framework for dynamic 3D reconstruction by marrying pointmap matching with temporal motion. Specifically, our method first learns an explicit matching relationship by mapping RGB pixels from both dynamic and static regions across different views to 3D pointmaps within a unified coordinate system. Furthermore, we introduce a temporal motion module for dynamic motions that ensures scale consistency across different frames and enhances performance in tasks requiring both precise geometry and reliable matching, most notably 3D point tracking. We show the effectiveness of the proposed pointmap matching and temporal fusion paradigm by demonstrating the remarkable performance across multiple downstream tasks, including video depth estimation, 3D point tracking, and pose estimation. Code and models are publicly available at https://github.com/wyddmw/POMATO.

Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice generative quality. We bridge this gap by proposing Structured Coupling for Flow Matching (SCFM), a cooperative framework that augments flow matching with structured latent representation learning. By introducing structured latent variables and exogenous noise into the source, SCFM jointly learns a structured prior (via latent variable modeling) and a continuous transport map (via flow matching). It uses a shared time-dependent recognition network for both latent variable model variational inference and intermediate-time flow velocity estimation. This yields a structurally informed yet unconditional, simulation-free flow model, where the latent variable model can also assist flow sampling. Empirically, SCFM facilitates unsupervised latent representation learning for clustering, disentanglement and downstream tasks, while remaining competitive with flow matching in sample quality, showing that meaningful structure can be learned without sacrificing generative fidelity.

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.

Flow-based generative models have become a strong framework for high-quality generative modeling, yet pretrained models are rarely used in their vanilla conditional form: conditional samples without guidance often appear diffuse and lack fine-grained detail due to the smoothing effects of neural networks. Existing guidance techniques such as classifier-free guidance (CFG) improve fidelity but double the inference cost and typically reduce sample diversity. We introduce Momentum Guidance (MG), a new dimension of guidance that leverages the ODE trajectory itself. MG extrapolates the current velocity using an exponential moving average of past velocities and preserves the standard one-evaluation-per-step cost. It matches the effect of standard guidance without extra computation and can further improve quality when combined with CFG. Experiments demonstrate MG's effectiveness across benchmarks. Specifically, on ImageNet-256, MG achieves average improvements in FID of 36.68% without CFG and 25.52% with CFG across various sampling settings, attaining an FID of 1.597 at 64 sampling steps. Evaluations on large flow-based models like Stable Diffusion 3 and FLUX.1-dev further confirm consistent quality enhancements across standard metrics.

LiDAR point clouds often contain motion-induced distortions, degrading the accuracy of object appearances in the captured data. In this paper, we first characterize the underlying reasons for the point cloud distortion and show that this is present in public datasets. We find that this distortion is more pronounced in high-speed environments such as highways, as well as in multi-LiDAR configurations, a common setup for heavy vehicles. Previous work has dealt with point cloud distortion from the ego-motion but fails to consider distortion from the motion of other objects. We therefore introduce a novel undistortion pipeline, HiMo, that leverages scene flow estimation for object motion compensation, correcting the depiction of dynamic objects. We further propose an extension of a state-of-the-art self-supervised scene flow method. Due to the lack of well-established motion distortion metrics in the literature, we also propose two metrics for compensation performance evaluation: compensation accuracy at a point level and shape similarity on objects. To demonstrate the efficacy of our method, we conduct extensive experiments on the Argoverse 2 dataset and a new real-world dataset. Our new dataset is collected from heavy vehicles equipped with multi-LiDARs and on highways as opposed to mostly urban settings in the existing datasets. The source code, including all methods and the evaluation data, will be provided upon publication. See https://kin-zhang.github.io/HiMo for more details.

This paper introduces MCTrack, a new 3D multi-object tracking method that achieves state-of-the-art (SOTA) performance across KITTI, nuScenes, and Waymo datasets. Addressing the gap in existing tracking paradigms, which often perform well on specific datasets but lack generalizability, MCTrack offers a unified solution. Additionally, we have standardized the format of perceptual results across various datasets, termed BaseVersion, facilitating researchers in the field of multi-object tracking (MOT) to concentrate on the core algorithmic development without the undue burden of data preprocessing. Finally, recognizing the limitations of current evaluation metrics, we propose a novel set that assesses motion information output, such as velocity and acceleration, crucial for downstream tasks. The source codes of the proposed method are available at this link: https://github.com/megvii-research/MCTrack}{https://github.com/megvii-research/MCTrack

In many robotics and VR/AR applications, fast camera motions cause a high level of motion blur, causing existing camera pose estimation methods to fail. In this work, we propose a novel framework that leverages motion blur as a rich cue for motion estimation rather than treating it as an unwanted artifact. Our approach works by predicting a dense motion flow field and a monocular depth map directly from a single motion-blurred image. We then recover the instantaneous camera velocity by solving a linear least squares problem under the small motion assumption. In essence, our method produces an IMU-like measurement that robustly captures fast and aggressive camera movements. To train our model, we construct a large-scale dataset with realistic synthetic motion blur derived from ScanNet++v2 and further refine our model by training end-to-end on real data using our fully differentiable pipeline. Extensive evaluations on real-world benchmarks demonstrate that our method achieves state-of-the-art angular and translational velocity estimates, outperforming current methods like MASt3R and COLMAP.

Significant advancements have been made in video generative models recently. Unlike image generation, video generation presents greater challenges, requiring not only generating high-quality frames but also ensuring temporal consistency across these frames. Despite the impressive progress, research on metrics for evaluating the quality of generated videos, especially concerning temporal and motion consistency, remains underexplored. To bridge this research gap, we propose Fr\'echet Video Motion Distance (FVMD) metric, which focuses on evaluating motion consistency in video generation. Specifically, we design explicit motion features based on key point tracking, and then measure the similarity between these features via the Fr\'echet distance. We conduct sensitivity analysis by injecting noise into real videos to verify the effectiveness of FVMD. Further, we carry out a large-scale human study, demonstrating that our metric effectively detects temporal noise and aligns better with human perceptions of generated video quality than existing metrics. Additionally, our motion features can consistently improve the performance of Video Quality Assessment (VQA) models, indicating that our approach is also applicable to unary video quality evaluation. Code is available at https://github.com/ljh0v0/FMD-frechet-motion-distance.

Generating full-body human gestures based on speech signals remains challenges on quality and speed. Existing approaches model different body regions such as body, legs and hands separately, which fail to capture the spatial interactions between them and result in unnatural and disjointed movements. Additionally, their autoregressive/diffusion-based pipelines show slow generation speed due to dozens of inference steps. To address these two challenges, we propose GestureLSM, a flow-matching-based approach for Co-Speech Gesture Generation with spatial-temporal modeling. Our method i) explicitly model the interaction of tokenized body regions through spatial and temporal attention, for generating coherent full-body gestures. ii) introduce the flow matching to enable more efficient sampling by explicitly modeling the latent velocity space. To overcome the suboptimal performance of flow matching baseline, we propose latent shortcut learning and beta distribution time stamp sampling during training to enhance gesture synthesis quality and accelerate inference. Combining the spatial-temporal modeling and improved flow matching-based framework, GestureLSM achieves state-of-the-art performance on BEAT2 while significantly reducing inference time compared to existing methods, highlighting its potential for enhancing digital humans and embodied agents in real-world applications. Project Page: https://andypinxinliu.github.io/GestureLSM

AI-generated videos (AIGVs) typically contain subtle temporal artifacts that arise from inter-frame inconsistencies rather than within individual frames. A detector that captures such artifacts should therefore benefit from video pretrained backbones over image only ones. In practice, however, video backbones with standard global readouts often fail to outperform strong image pretrained probes on AIGV benchmarks. We attribute this gap to excessive spatiotemporal aggregation in the readout. Video pretrained backbones tend to compress each frame into a single global descriptor. This compression suppresses local patch level temporal dynamics and discards inter patch relations, which are precisely the cues that AIGV detection most reliably depends on. Based on this, we propose Velocity Gated Patch Velocity Profiling (V-PVP), a lightweight readout that replaces only the aggregation layer with two parallel streams over the patch velocity field, adding only about 0.5M trainable parameters. V-PVP serves as a general plug-and-play module that consistently improves performance across diverse video backbones under both end-to-end fine-tuning and linear probing settings. Our method reaches 95.28 AUC on AIGVDBench while keeping the backbone fully frozen. The results show that simply replacing the aggregation layer reactivates the temporal potential of frozen video backbones, restoring their advantage on AIGV detection. Code is available at https://anonymous.4open.science/r/PVP-81B3/.

Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled efficient one-step or few-step generation, yet despite their practical success, a systematic understanding of their design has been hindered by the lack of a comprehensive theoretical framework. Here we introduce Flow Map Matching (FMM), a principled framework for learning the two-time flow map of an underlying dynamical generative model, thereby providing this missing mathematical foundation. Leveraging stochastic interpolants, we propose training objectives both for distillation from a pre-trained velocity field and for direct training of a flow map over an interpolant or a forward diffusion process. Theoretically, we show that FMM unifies and extends a broad class of existing approaches for fast sampling, including consistency models, consistency trajectory models, and progressive distillation. Experiments on CIFAR-10 and ImageNet-32 highlight that our approach can achieve sample quality comparable to flow matching while reducing generation time by a factor of 10-20.

Video Moment Retrieval is a task in video understanding that aims to localize a specific temporal segment in an untrimmed video based on a natural language query. Despite recent progress in moment retrieval from videos using both traditional techniques and Multimodal Large Language Models (MLLM), most existing methods still rely on coarse temporal understanding and a single visual modality, limiting performance on complex videos. To address this, we introduce Shot-aware Multimodal Audio-enhanced Retrieval of Temporal Segments (SMART), an MLLM-based framework that integrates audio cues and leverages shot-level temporal structure. SMART enriches multimodal representations by combining audio and visual features while applying Shot-aware Token Compression, which selectively retains high-information tokens within each shot to reduce redundancy and preserve fine-grained temporal details. We also refine prompt design to better utilize audio-visual cues. Evaluations on Charades-STA and QVHighlights show that SMART achieves significant improvements over state-of-the-art methods, including a 1.61\% increase in R1@0.5 and 2.59\% gain in R1@0.7 on Charades-STA.

A reliable and accurate 3D tracking framework is essential for predicting future locations of surrounding objects and planning the observer's actions in numerous applications such as autonomous driving. We propose a framework that can effectively associate moving objects over time and estimate their full 3D bounding box information from a sequence of 2D images captured on a moving platform. The object association leverages quasi-dense similarity learning to identify objects in various poses and viewpoints with appearance cues only. After initial 2D association, we further utilize 3D bounding boxes depth-ordering heuristics for robust instance association and motion-based 3D trajectory prediction for re-identification of occluded vehicles. In the end, an LSTM-based object velocity learning module aggregates the long-term trajectory information for more accurate motion extrapolation. Experiments on our proposed simulation data and real-world benchmarks, including KITTI, nuScenes, and Waymo datasets, show that our tracking framework offers robust object association and tracking on urban-driving scenarios. On the Waymo Open benchmark, we establish the first camera-only baseline in the 3D tracking and 3D detection challenges. Our quasi-dense 3D tracking pipeline achieves impressive improvements on the nuScenes 3D tracking benchmark with near five times tracking accuracy of the best vision-only submission among all published methods. Our code, data and trained models are available at https://github.com/SysCV/qd-3dt.

We address the problem of retrieving a specific moment from an untrimmed video by a query sentence. This is a challenging problem because a target moment may take place in relations to other temporal moments in the untrimmed video. Existing methods cannot tackle this challenge well since they consider temporal moments individually and neglect the temporal dependencies. In this paper, we model the temporal relations between video moments by a two-dimensional map, where one dimension indicates the starting time of a moment and the other indicates the end time. This 2D temporal map can cover diverse video moments with different lengths, while representing their adjacent relations. Based on the 2D map, we propose a Temporal Adjacent Network (2D-TAN), a single-shot framework for moment localization. It is capable of encoding the adjacent temporal relation, while learning discriminative features for matching video moments with referring expressions. We evaluate the proposed 2D-TAN on three challenging benchmarks, i.e., Charades-STA, ActivityNet Captions, and TACoS, where our 2D-TAN outperforms the state-of-the-art.

Given a query, the task of Natural Language Video Localization (NLVL) is to localize a temporal moment in an untrimmed video that semantically matches the query. In this paper, we adopt a proposal-based solution that generates proposals (i.e., candidate moments) and then select the best matching proposal. On top of modeling the cross-modal interaction between candidate moments and the query, our proposed Moment Sampling DETR (MS-DETR) enables efficient moment-moment relation modeling. The core idea is to sample a subset of moments guided by the learnable templates with an adopted DETR (DEtection TRansformer) framework. To achieve this, we design a multi-scale visual-linguistic encoder, and an anchor-guided moment decoder paired with a set of learnable templates. Experimental results on three public datasets demonstrate the superior performance of MS-DETR.

High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation. While Conditional Flow Matching (CFM) offers a robust acceleration approach, we demonstrate its standard training loss is fundamentally misleading. Specifically, utilizing a Jefferson Lab Nuclear Physics (NP) kinematic dataset (γp to ρ^0 p to π^+π^- p), we expose that CFM loss plateaus prematurely, obscuring ongoing physical refinement. To verify this disconnect is a dataset-agnostic pathology, we introduce ScatterPrism, an efficient generative surrogate evaluated against both the NP data and synthetic stress tests modeling challenging 1D distribution topologies. Coupling these benchmarks, we establish that physics-informed metrics continue improving long after standard loss converges. Consequently, we propose a multi-metric diagnostic protocol to ensure true kinematic fidelity without data memorization. Driven by NP challenges relevant to the forthcoming Electron-Ion Collider (EIC), this unified machinery has strong potential to extend to High-Energy Physics (HEP) applications, such as jet modeling. Furthermore, the framework holds promise for broader domains requiring rigorous generative reliability, including medical imaging, astrophysics, and quantitative finance.

Recently, efficient fine-tuning of large-scale pre-trained models has attracted increasing research interests, where linear probing (LP) as a fundamental module is involved in exploiting the final representations for task-dependent classification. However, most of the existing methods focus on how to effectively introduce a few of learnable parameters, and little work pays attention to the commonly used LP module. In this paper, we propose a novel Moment Probing (MP) method to further explore the potential of LP. Distinguished from LP which builds a linear classification head based on the mean of final features (e.g., word tokens for ViT) or classification tokens, our MP performs a linear classifier on feature distribution, which provides the stronger representation ability by exploiting richer statistical information inherent in features. Specifically, we represent feature distribution by its characteristic function, which is efficiently approximated by using first- and second-order moments of features. Furthermore, we propose a multi-head convolutional cross-covariance (MHC^3) to compute second-order moments in an efficient and effective manner. By considering that MP could affect feature learning, we introduce a partially shared module to learn two recalibrating parameters (PSRP) for backbones based on MP, namely MP_{+}. Extensive experiments on ten benchmarks using various models show that our MP significantly outperforms LP and is competitive with counterparts at less training cost, while our MP_{+} achieves state-of-the-art performance.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

We introduce the task of retrieving relevant video moments from a large corpus of untrimmed, unsegmented videos given a natural language query. Our task poses unique challenges as a system must efficiently identify both the relevant videos and localize the relevant moments in the videos. To address these challenges, we propose SpatioTemporal Alignment with Language (STAL), a model that represents a video moment as a set of regions within a series of short video clips and aligns a natural language query to the moment's regions. Our alignment cost compares variable-length language and video features using symmetric squared Chamfer distance, which allows for efficient indexing and retrieval of the video moments. Moreover, aligning language features to regions within a video moment allows for finer alignment compared to methods that extract only an aggregate feature from the entire video moment. We evaluate our approach on two recently proposed datasets for temporal localization of moments in video with natural language (DiDeMo and Charades-STA) extended to our video corpus moment retrieval setting. We show that our STAL re-ranking model outperforms the recently proposed Moment Context Network on all criteria across all datasets on our proposed task, obtaining relative gains of 37% - 118% for average recall and up to 30% for median rank. Moreover, our approach achieves more than 130x faster retrieval and 8x smaller index size with a 1M video corpus in an approximate setting.

Classifier-free guidance (CFG) typically applies a shared scale to all latent tokens, although their velocity predictions evolve differently during sampling. We introduce Trajectory-Adaptive Classifier-Free Guidance (TrajCFG), a training-free method for flow-matching models that adapts token-wise guidance using historical changes in guided velocity direction. TrajCFG maps this feedback to bounded scales, assigning stronger guidance to larger directional changes and weaker guidance to more consistent directions. It combines adjacent-step and interval-normalized longer-span feedback, reusing standard CFG predictions without additional model evaluations. Controlled diagnostics and ablations examine the roles of directional feedback, token-wise allocation, and history-span fusion. Experiments on text-to-video, image-to-video, text-to-audio-video, text-to-image, and image-to-3D generation show improvements over base samplers across multiple backbones. For text-to-video generation, TrajCFG improves VBench Total scores by 0.30-0.75 points over the strongest evaluated baseline on each of three backbones. These results support historical directional feedback as a broadly applicable signal for fine-grained guidance allocation. The project page is available at https://jyliu-98.github.io/trajcfg-project-page/.

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed covariance moment matching technique and introduce a novel method for learning the diagonal covariance. Unlike traditional data-driven diagonal covariance approximation approaches, our method involves directly regressing the optimal diagonal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency, recall rate and likelihood of commonly used diffusion models.

Generative models like Flow Matching have achieved state-of-the-art performance but are often hindered by a computationally expensive iterative sampling process. To address this, recent work has focused on few-step or one-step generation by learning the average velocity field, which directly maps noise to data. MeanFlow, a leading method in this area, learns this field by enforcing a differential identity that connects the average and instantaneous velocities. In this work, we argue that this differential formulation is a limiting special case of a more fundamental principle. We return to the first principles of average velocity and leverage the additivity property of definite integrals. This leads us to derive a novel, purely algebraic identity we term Interval Splitting Consistency. This identity establishes a self-referential relationship for the average velocity field across different time intervals without resorting to any differential operators. Based on this principle, we introduce SplitMeanFlow, a new training framework that enforces this algebraic consistency directly as a learning objective. We formally prove that the differential identity at the core of MeanFlow is recovered by taking the limit of our algebraic consistency as the interval split becomes infinitesimal. This establishes SplitMeanFlow as a direct and more general foundation for learning average velocity fields. From a practical standpoint, our algebraic approach is significantly more efficient, as it eliminates the need for JVP computations, resulting in simpler implementation, more stable training, and broader hardware compatibility. One-step and two-step SplitMeanFlow models have been successfully deployed in large-scale speech synthesis products (such as Doubao), achieving speedups of 20x.

We propose a training recipe that treats charged-particle trajectory parameter regression on high-energy physics detector data as a sequence-modeling task. Kalman filters and linearized least-squares fits have been the classical standard approach for this task: they are optimal estimators for sparsely sampled linear-Gaussian data and are commonly used for trajectory parameter regression (fitting). The classical fitting techniques implemented for this domain reach a final precision of one part in 10^5 through detailed modeling of detector geometry, material, detection effects and precise numerical integration of the equations of motion through the detector's inhomogeneous magnetic field. With this study, we demonstrate that using a bidirectional gated linear recurrent encoder, one is able to reproduce the full precision of classical track fitting techniques. Using a custom kernel, we also achieve significantly higher throughput during GPU inference, compared to classical fitting software running on similarly priced multi-core CPU servers representing typically employed hardware. Such a speedup would lead to considerable cost savings for the pattern recognition at the Large Hadron Collider. To our knowledge, this is the first end-to-end learned track fit to reach the full precision and, at the same time, offer the opportunity to reduce the computing costs.

Mobility simulation supports logistics, safety, and communications planning in industrial environments such as ports, mines, and airports. Existing trajectory models, however, rely on absolute coordinates, road-network tokens, or semantic zones: representations that are site-specific and not well suited to unstructured industrial terrain. We introduce the Industrial Kinematic Trajectory Model (IKTM), a coordinate-free trajectory generator that represents industrial vehicle motion through kinematic sequences (speed and heading change) with no absolute spatial reference. IKTM uses an autoregressive causal transformer with probabilistic mixture heads and extends our prior coordinate-free Markovian model with deep sequence modelling and an explicit duration-conditioning signal. Trained on one site and evaluated zero-shot on three unseen sites, it matches the small-turn shape of the empirical turn-rate distributions of held-out telematics; across all four sites, the per-site mean Jensen-Shannon divergence over 100 sampling seeds spans approximately 0.035-0.050 bits under an oracle-length duration-target protocol and approximately 0.032-0.042 bits under a fully zero-shot prior-length protocol, with similar ranges whether out-of-distribution (OOD) duration targets are drawn from each held-out site's empirical length distribution or from the Site A prior. Both protocols stay above the metric's sampling-noise floor (<=0.0049 bits). Paired by site, the oracle-length values are 5.3-6.0x lower than those of a re-implementation of our prior Markovian model under the same 1 Hz protocol. Termination is duration-conditioned rather than spatial: rollouts stop on 100% of trials with a length-tracking error of +0.0 +/- 0.0 s against the sampled target (100 of 100 exactly on target; N=100, T=0.2, untouched in-distribution test split).

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9times) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.

Diffusion models (DMs) and flow-matching models have demonstrated remarkable performance in image and video generation. However, such models require a significant number of function evaluations (NFEs) during sampling, leading to costly inference. Consequently, quality-preserving fast sampling methods that require fewer NFEs have been an active area of research. However, prior training-free sampling methods fail to simultaneously address two key challenges: the stiffness of the ODE (i.e., the non-straightness of the velocity field) and dependence on the semi-linear structure of the DM ODE (which limits their direct applicability to flow-matching models). In this work, we introduce the Stabilized Taylor Orthogonal Runge--Kutta (STORK) method, addressing both design concerns. We demonstrate that STORK consistently improves the quality of diffusion and flow-matching sampling for image and video generation. Code is available at https://github.com/ZT220501/STORK.

Single frame data contains finite information which limits the performance of the existing vision-based multi-camera 3D object detection paradigms. For fundamentally pushing the performance boundary in this area, a novel paradigm dubbed BEVDet4D is proposed to lift the scalable BEVDet paradigm from the spatial-only 3D space to the spatial-temporal 4D space. We upgrade the naive BEVDet framework with a few modifications just for fusing the feature from the previous frame with the corresponding one in the current frame. In this way, with negligible additional computing budget, we enable BEVDet4D to access the temporal cues by querying and comparing the two candidate features. Beyond this, we simplify the task of velocity prediction by removing the factors of ego-motion and time in the learning target. As a result, BEVDet4D with robust generalization performance reduces the velocity error by up to -62.9%. This makes the vision-based methods, for the first time, become comparable with those relied on LiDAR or radar in this aspect. On challenge benchmark nuScenes, we report a new record of 54.5% NDS with the high-performance configuration dubbed BEVDet4D-Base, which surpasses the previous leading method BEVDet-Base by +7.3% NDS. The source code is publicly available for further research at https://github.com/HuangJunJie2017/BEVDet .

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from scratch. By analyzing the relationship between the velocity function and the solution function of the velocity ordinary differential equation (ODE), we propose a Flow Matching loss and a solution consistency loss to train our models. The Flow Matching loss allows our models to provide estimated velocity fields for Classifier-Free Guidance (CFG) during training, which improves generation performance. Notably, our consistency loss does not require the calculation of the Jacobian-vector product (JVP), a common requirement in recent works that is not well-optimized in deep learning frameworks like PyTorch. Experimental results indicate that, when trained from scratch using the same Diffusion Transformer (DiT) architecture and an equal number of training epochs, our models achieve better FID-50K scores than MeanFlow models on the ImageNet 256x256 dataset.

Recent diffusion and flow matching models have demonstrated strong capabilities in image generation and editing by progressively removing noise through iterative sampling. While this enables flexible inversion for semantic-preserving edits, few-step sampling regimes suffer from poor forward process approximation, leading to degraded editing quality. Existing few-step inversion methods often rely on pretrained generators and auxiliary modules, limiting scalability and generalization across different architectures. To address these limitations, we propose BiFM (Bidirectional Flow Matching), a unified framework that jointly learns generation and inversion within a single model. BiFM directly estimates average velocity fields in both ``image to noise" and ``noise to image" directions, constrained by a shared instantaneous velocity field derived from either predefined schedules or pretrained multi-step diffusion models. Additionally, BiFM introduces a novel training strategy using continuous time-interval supervision, stabilized by a bidirectional consistency objective and a lightweight time-interval embedding. This bidirectional formulation also enables one-step inversion and can integrate seamlessly into popular diffusion and flow matching backbones. Across diverse image editing and generation tasks, BiFM consistently outperforms existing few-step approaches, achieving superior performance and editability.

We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models and instead learns the equilibrium gradient of an implicit energy landscape. Through this approach, we can adopt an optimization-based sampling process at inference time, where samples are obtained by gradient descent on the learned landscape with adjustable step sizes, adaptive optimizers, and adaptive compute. EqM surpasses the generation performance of diffusion/flow models empirically, achieving an FID of 1.90 on ImageNet 256times256. EqM is also theoretically justified to learn and sample from the data manifold. Beyond generation, EqM is a flexible framework that naturally handles tasks including partially noised image denoising, OOD detection, and image composition. By replacing time-conditional velocities with a unified equilibrium landscape, EqM offers a tighter bridge between flow and energy-based models and a simple route to optimization-driven inference.

Diffusion and flow-matching schedules control the signal and noise coefficients that mix data and noise along affine probability paths. Minimizing a kinetic action defined on coefficient paths, motivated by optimal transport, helps explain strong baselines but remains model-agnostic and ignores prediction error. Here we introduce a model-aware schedule construction based on fiberwise optimal transport. At a fixed time and state on the probability path, compatible signal/noise decompositions form an affine fiber. We define a fiberwise prediction risk by averaging optimal-transport costs between the true and predictor-induced decompositions within these fibers. On a fixed coefficient curve, combining this risk with coefficient-path kinetic action yields a closed-form optimal time allocation. This construction extends to general linear prediction targets, and the risk profile can be estimated from an early baseline checkpoint. We evaluate DDPMs and flow matching across prediction targets, training configurations, risk-estimation checkpoints, datasets, and architectures. Our model-aware schedules consistently outperform strong baselines, including a 38.6% relative FID reduction for flow matching on CIFAR-10 at 16 function evaluations. Each model-agnostic kinetic baseline determines its own kinetic reference coordinate. In these coordinates, fiberwise-risk profiles from independently trained models in different settings align closely after normalization to unit area. The resulting schedule deformations used in training also align, suggesting empirical universality across the evaluated models and settings. Pretrained-checkpoint diagnostics extend this normalized-risk agreement to larger conditional latent diffusion and 2-RF models. A frozen analytic allocation template retains most of the model-aware improvement without further risk estimation or model-specific fitting.

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.

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

Temporal Action Detection (TAD) focuses on detecting pre-defined actions, while Moment Retrieval (MR) aims to identify the events described by open-ended natural language within untrimmed videos. Despite that they focus on different events, we observe they have a significant connection. For instance, most descriptions in MR involve multiple actions from TAD. In this paper, we aim to investigate the potential synergy between TAD and MR. Firstly, we propose a unified architecture, termed Unified Moment Detection (UniMD), for both TAD and MR. It transforms the inputs of the two tasks, namely actions for TAD or events for MR, into a common embedding space, and utilizes two novel query-dependent decoders to generate a uniform output of classification score and temporal segments. Secondly, we explore the efficacy of two task fusion learning approaches, pre-training and co-training, in order to enhance the mutual benefits between TAD and MR. Extensive experiments demonstrate that the proposed task fusion learning scheme enables the two tasks to help each other and outperform the separately trained counterparts. Impressively, UniMD achieves state-of-the-art results on three paired datasets Ego4D, Charades-STA, and ActivityNet. Our code is available at https://github.com/yingsen1/UniMD.

Orbit recovery problems are a class of problems that often arise in practice and various forms. In these problems, we aim to estimate an unknown function after being distorted by a group action and observed via a known operator. Typically, the observations are contaminated with a non-trivial level of noise. Two particular orbit recovery problems of interest in this paper are multireference alignment and single-particle cryo-EM modelling. In order to suppress the noise, we suggest using the method of moments approach for both problems while introducing deep neural network priors. In particular, our neural networks should output the signals and the distribution of group elements, with moments being the input. In the multireference alignment case, we demonstrate the advantage of using the NN to accelerate the convergence for the reconstruction of signals from the moments. Finally, we use our method to reconstruct simulated and biological volumes in the cryo-EM setting.

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.

Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods. Existing density-approximated policy gradient methods rely on stochastic SDE samplers to construct tractable transition kernels, which introduce training-inference inconsistencies and necessitates Classifier-Free Guidance (CFG). While implicit frameworks such as DiffusionNFT directly optimize forward-process velocity fields, its heuristic fixed-magnitude corrections prevent optimization strength from relative intra-group quality. We propose Flow Advantage-Weighted Rectification (FlowAWR), a paradigm that recasts continuous generative policy optimization as supervised regression toward a theoretically optimal velocity field. Starting from the optimal policy of a KL-constrained reward maximization, FlowAWR derives the optimal velocity field that admits a magnitude-aware, advantage-weighted rectification form, yielding SDE-free optimization and CFG-free generation. In comparative evaluations on SD3.5-Medium, FlowAWR achieves improved alignment performance alongside a 2times to 5times convergence acceleration over DiffusionNFT (e.g., reaching a 24.12 PickScore in 1.2k steps, versus 23.82 in 2.0k steps for DiffusionNFT and 23.50 in >4k steps for FlowGRPO). Under multi-reward constraints, FlowAWR sustains generation quality, satisfying structural rules while maintaining stable out-of-domain performance.

Referring Video Object Segmentation (RefVOS) seeks to segment target objects in videos guided by natural language descriptions, demanding both temporal reasoning and fine-grained visual comprehension. Existing sampling strategies for LLM-based approaches typically rely on either handcrafted heuristics or external keyframe models. The former often overlooks essential temporal cues, while the latter increases system complexity. To address this, we propose a unified framework that jointly optimizes Temporal Sentence Grounding (TSG) and RefVOS, naturally incorporating key moment grounding capability. During training, we introduce a novel TSG paradigm that employs a dedicated [FIND] token for key moment identification through temporal token similarity matching, thereby avoiding the need for external timestamp encodings. For inference, we design a Moment-Centric Sampling (MCS) strategy that densely samples informative moments while sparsely sampling non-essential frames, preserving both motion details and global context. To further enhance tracking stability, we develop Bidirectional Anchor-updated Propagation (BAP), which leverages the most relevant moment as start point for high-quality mask initialization and dynamically updates at sampled points to mitigate accumulated errors. Code and model will be available at: https://github.com/Dmmm1997/MomentSeg

This paper introduces SFSORT, the world's fastest multi-object tracking system based on experiments conducted on MOT Challenge datasets. To achieve an accurate and computationally efficient tracker, this paper employs a tracking-by-detection method, following the online real-time tracking approach established in prior literature. By introducing a novel cost function called the Bounding Box Similarity Index, this work eliminates the Kalman Filter, leading to reduced computational requirements. Additionally, this paper demonstrates the impact of scene features on enhancing object-track association and improving track post-processing. Using a 2.2 GHz Intel Xeon CPU, the proposed method achieves an HOTA of 61.7\% with a processing speed of 2242 Hz on the MOT17 dataset and an HOTA of 60.9\% with a processing speed of 304 Hz on the MOT20 dataset. The tracker's source code, fine-tuned object detection model, and tutorials are available at https://github.com/gitmehrdad/SFSORT.

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.

Existing generative models for 3D shapes can synthesize high-fidelity and visually plausible shapes. For certain classes of shapes that have undergone an engineering design process, the realism of the shape is tightly coupled with the underlying physical properties, e.g., aerodynamic efficiency for automobiles. Since existing methods lack knowledge of such physics, they are unable to use this knowledge to enhance the realism of shape generation. Motivated by this, we propose a unified physics-based 3D shape generation pipeline, with a focus on industrial design applications. Specifically, we introduce a new flow matching model with explicit physical guidance, consisting of an alternating update process. We iteratively perform a velocity-based update and a physics-based refinement, progressively adjusting the latent code to align with the desired 3D shapes and physical properties. We further strengthen physical validity by incorporating a physics-aware regularization term into the velocity-based update step. To support such physics-guided updates, we build a shape-and-physics variational autoencoder (SP-VAE) that jointly encodes shape and physics information into a unified latent space. The experiments on three benchmarks show that this synergistic formulation improves shape realism beyond mere visual plausibility.

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

Few-step distillation reduces the sampling cost of diffusion and flow models, but existing approaches often require auxiliary score models or specialized architectures. We show that simple on-policy velocity regression already provides a strong foundation for 4-NFE generation. To represent teacher velocity variation within each coarse transition, we introduce Pivot, a training-only residual proxy that separates local corrections from the student's interval-mean prediction. We further repel the student from weaker teacher predictions, providing a lightweight mechanism for avoiding undesirable modes. The resulting framework, Simplified Matching Distillation (SMD), remains entirely regression-based, requires neither online score estimation nor adversarial training, and leaves the deployed generator unchanged. We evaluate SMD on image generation and editing, 3D generation, video synthesis, and joint audio--video generation, scaling to 33 billion parameters. At 4-NFE, SMD outperforms strong few-step baselines and surpasses multi-step teachers on several benchmarks. It also supports cross-model, multi-teacher, and causal-video distillation.

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the Flux Matching objective imposes a weaker condition that admits infinitely many vector fields whose stationary distribution is the data. This flexibility enables a class of generative models that cannot be learned under score matching, in which inductive biases, structural priors, and properties of the dynamics can be directly imposed or optimized. We show that Flux Matching performs strongly on high-dimensional image datasets and, more importantly, that our added freedom unlocks a range of applications including faster sampling, interpretable and mechanistic models, and dynamics that encode directed dependencies between variables. More broadly, Flux Matching opens a new dimension in generative modeling by turning the vector field itself into a design choice rather than a fixed target. Code is available at https://github.com/peterpaohuang/flux_matching.

Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that na\"ive linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in O(L) speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.

One-step generative modeling seeks to generate high-quality data samples in a single function evaluation, significantly improving efficiency over traditional diffusion or flow-based models. In this work, we introduce Modular MeanFlow (MMF), a flexible and theoretically grounded approach for learning time-averaged velocity fields. Our method derives a family of loss functions based on a differential identity linking instantaneous and average velocities, and incorporates a gradient modulation mechanism that enables stable training without sacrificing expressiveness. We further propose a curriculum-style warmup schedule to smoothly transition from coarse supervision to fully differentiable training. The MMF formulation unifies and generalizes existing consistency-based and flow-matching methods, while avoiding expensive higher-order derivatives. Empirical results across image synthesis and trajectory modeling tasks demonstrate that MMF achieves competitive sample quality, robust convergence, and strong generalization, particularly under low-data or out-of-distribution settings.

DiffusionNFT (NFT) fine-tunes diffusion models toward task-specific rewards, but optimizing these rewards does not guarantee fidelity to the full prompt. Although classifier-free guidance (CFG) strengthens prompt alignment, NFT is formulated as a CFG-free method, and applying CFG to the fine-tuned velocity field can reduce the optimized reward. This motivates optimizing rewards over the guided output distribution while seeking to retain its prompt alignment. However, applying standard NFT directly to guided samples can cause reward degradation or training collapse. We trace this failure to a mismatch between the reference velocity used in the NFT loss and the score of the guided sample distribution, which biases the improvement direction. We propose GuidanceNFT, which estimates the matching reference velocity through online flow matching on guided samples and uses it to correct both regression terms. With an exact reference, the corrected objective recovers NFT's intended update. In our experiments, the learned correction sustains reward improvement under both explicit and built-in guidance. On SD3.5-M, GuidanceNFT achieves higher optimized rewards than NFT with and without CFG across GenEval, text-rendering, and multi-reward objectives, together with better overall prompt alignment as measured by off-domain evaluation metrics. Experiments on models with built-in guidance, including Model Guidance and ELF, further demonstrate improved ImageNet generation, a better perplexity-entropy tradeoff on OpenWebText, and higher accuracy on GSM8K.

We present a new test-time optimization method for estimating dense and long-range motion from a video sequence. Prior optical flow or particle video tracking algorithms typically operate within limited temporal windows, struggling to track through occlusions and maintain global consistency of estimated motion trajectories. We propose a complete and globally consistent motion representation, dubbed OmniMotion, that allows for accurate, full-length motion estimation of every pixel in a video. OmniMotion represents a video using a quasi-3D canonical volume and performs pixel-wise tracking via bijections between local and canonical space. This representation allows us to ensure global consistency, track through occlusions, and model any combination of camera and object motion. Extensive evaluations on the TAP-Vid benchmark and real-world footage show that our approach outperforms prior state-of-the-art methods by a large margin both quantitatively and qualitatively. See our project page for more results: http://omnimotion.github.io/

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere mathbb S^{d-1}. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on mathbb S^{d-1} to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on (mathbb S^{d-1})^L both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.

Adaptive moment methods such as Adam use a diagonal, coordinate-wise preconditioner based on exponential moving averages of squared gradients. This diagonal scaling is coordinate-system dependent and can struggle with dense or rotated parameter couplings, including those in matrix factorization, tensor decomposition, and graph neural networks, because it treats each parameter independently. We introduce FlowAdam, a hybrid optimizer that augments Adam with continuous gradient-flow integration via an ordinary differential equation (ODE). When EMA-based statistics detect landscape difficulty, FlowAdam switches to clipped ODE integration. Our central contribution is Soft Momentum Injection, which blends ODE velocity with Adam's momentum during mode transitions. This prevents the training collapse observed with naive hybrid approaches. Across coupled optimization benchmarks, the ODE integration provides implicit regularization, reducing held-out error by 10-22% on low-rank matrix/tensor recovery and 6% on Jester (real-world collaborative filtering), also surpassing tuned Lion and AdaBelief, while matching Adam on well-conditioned workloads (CIFAR-10). MovieLens-100K confirms benefits arise specifically from coupled parameter interactions rather than bias estimation. Ablation studies show that soft injection is essential, as hard replacement reduces accuracy from 100% to 82.5%.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

We present Generative Anchored Fields (GAF), a generative model that learns independent endpoint predictors, J (noise) and K (data), from any point on a linear bridge. Unlike existing approaches that use a single trajectory or score predictor, GAF is trained to recover the bridge endpoints directly via coordinate learning. The velocity field v=K-J emerges from their time-conditioned disagreement. This factorization enables Transport Algebra: algebraic operations on multiple J/K heads for compositional control. With class-specific K_n heads, GAF defines directed transport maps between a shared base noise distribution and multiple data domains, allowing controllable interpolation, multi-class composition, and semantic editing. This is achieved either directly on the predicted data coordinates (K) using Iterative Endpoint Refinement (IER), a novel sampler that achieves high-quality generation in 5-8 steps, or on the emergent velocity field (v). We achieve strong sample quality (FID 7.51 on ImageNet 256times256 and 7.27 on CelebA-HQ 256times 256, without classifier-free guidance) while treating compositional generation as an architectural primitive. Code available at https://github.com/IDLabMedia/GAF.

This paper focuses on a novel approach for detecting moving objects during camera motion. We present an optical-flow-based transformation that yields a consistent 2D invariant image output regardless of time instants, range of points in 3D, and the speed of the camera. In other words, this transformation generates a lookup image that remains invariant despite the changing projection of the 3D scene and camera motion. In the new domain, projections of 3D points that deviate from the values of the predefined lookup image can be clearly identified as moving relative to the stationary 3D environment, making them seamlessly detectable. The method does not require prior knowledge of the direction of motion or speed of the camera, nor does it necessitate 3D point range information. It is well-suited for real-time parallel processing, rendering it highly practical for implementation. We have validated the effectiveness of the new domain through simulations and experiments, demonstrating its robustness in scenarios involving rectilinear camera motion, both in simulations and with real-world data. This approach introduces new ways for moving objects detection during camera motion, and also lays the foundation for future research in the context of moving object detection during six-degrees-of-freedom camera motion.

Visual teach-and-repeat (VT&R) navigation enables robots to autonomously traverse previously demonstrated paths using visual feedback. We present a novel event-camera-based VT\&R system. Our system formulates event-stream matching as frequency-domain cross-correlation, transforming spatial convolutions into efficient Fourier-space multiplications. By exploiting the binary structure of event frames and applying image compression techniques, we achieve a processing latency of just 2.88 ms, about 3.5 times faster than conventional camera-based baselines that are optimised for runtime efficiency. Experiments using a Prophesee EVK4 HD event camera mounted on an AgileX Scout Mini robot demonstrate successful autonomous navigation across 3000+ meters of indoor and outdoor trajectories in daytime and nighttime conditions. Our system maintains Cross-Track Errors (XTE) below 15 cm, demonstrating the practical viability of event-based perception for real-time VT\&R navigation.

Dataset distillation has emerged as a powerful approach for reducing data requirements in deep learning. Among various methods, distribution matching-based approaches stand out for their balance of computational efficiency and strong performance. However, existing distance metrics used in distribution matching often fail to accurately capture distributional differences, leading to unreliable measures of discrepancy. In this paper, we reformulate dataset distillation as a minmax optimization problem and introduce Neural Characteristic Function Discrepancy (NCFD), a comprehensive and theoretically grounded metric for measuring distributional differences. NCFD leverages the Characteristic Function (CF) to encapsulate full distributional information, employing a neural network to optimize the sampling strategy for the CF's frequency arguments, thereby maximizing the discrepancy to enhance distance estimation. Simultaneously, we minimize the difference between real and synthetic data under this optimized NCFD measure. Our approach, termed Neural Characteristic Function Matching (), inherently aligns the phase and amplitude of neural features in the complex plane for both real and synthetic data, achieving a balance between realism and diversity in synthetic samples. Experiments demonstrate that our method achieves significant performance gains over state-of-the-art methods on both low- and high-resolution datasets. Notably, we achieve a 20.5\% accuracy boost on ImageSquawk. Our method also reduces GPU memory usage by over 300times and achieves 20times faster processing speeds compared to state-of-the-art methods. To the best of our knowledge, this is the first work to achieve lossless compression of CIFAR-100 on a single NVIDIA 2080 Ti GPU using only 2.3 GB of memory.

This paper presents a novel approach to Visual Inertial Odometry (VIO), focusing on the initialization and feature matching modules. Existing methods for initialization often suffer from either poor stability in visual Structure from Motion (SfM) or fragility in solving a huge number of parameters simultaneously. To address these challenges, we propose a new pipeline for visual inertial initialization that robustly handles various complex scenarios. By tightly coupling gyroscope measurements, we enhance the robustness and accuracy of visual SfM. Our method demonstrates stable performance even with only four image frames, yielding competitive results. In terms of feature matching, we introduce a hybrid method that combines optical flow and descriptor-based matching. By leveraging the robustness of continuous optical flow tracking and the accuracy of descriptor matching, our approach achieves efficient, accurate, and robust tracking results. Through evaluation on multiple benchmarks, our method demonstrates state-of-the-art performance in terms of accuracy and success rate. Additionally, a video demonstration on mobile devices showcases the practical applicability of our approach in the field of Augmented Reality/Virtual Reality (AR/VR).