Flow Matching

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79 papers in the last four weeks, up 365% on the four weeks before. 0.8% of all new papers.

Jul 13Week of Sep 28

Latest papers 446

Sep 30, 2026cs.LG

Correcting CondOT: Exact Finite-Step Sampling in Gaussian Flow Matching

Flow matching generates samples by gradually transforming noise into data. In practice, using a finite number of sampling steps introduces a numerical error that depends on the chosen schedule. We study this dependence for Gaussian targets and the explicit midpoint sampling method, using the exact flow field. We measure sampling error by the squared Wasserstein distance between the target distribution and the final distribution produced by the midpoint sampler. We show that the standard conditional optimal transport (CondOT) schedule cancels the leading midpoint error and improves the general convergence bound, even when the sampling steps are unequally spaced. On a uniform grid of

S

sampling steps, we fix the signal schedule at

α_t=t

and prove the existence of scalar noise schedules

β_t

that approach the CondOT noise schedule

1-t

at rate

1/S

and yield exact Gaussian sampling for every sufficiently large

S

. Controlled Gaussian experiments illustrate the convergence rates and exact calibration.

Ron Levy, Michael Elad

Department of Computer Science Technion, Israel

Flow Matching Diffusion Sampling Flow-Based Generative Modeling Optimal Transport

Sep 30, 2026cs.AI

SkillFM: Generating Skills for LLM Agents via Latent Flow Matching

Textual skills provide reusable guidance for large language model agents, but existing approaches often rely on manually curated skill banks or reinforcement learning with indirect and delayed feedback. We introduce SkillFM (Skill Flow Matching), a generative framework that synthesizes task-conditioned textual skills directly without test-time skill retrieval. Our framework combines a codec for encoding and reconstructing textual skills in a continuous latent space with a conditional flow model trained using improved MeanFlow. At inference time, the learned velocity field enables single-step latent sampling, and an LLM-based decoder converts the sampled representation into textual guidance for a frozen downstream agent. We evaluate the framework on embodied tasks, question answering, and web shopping. On ALFWorld and Search-QA, our method achieves the best overall performance among the compared vector-based skill approaches. Our analyses further demonstrate that latent skill generation is an effective alternative to retrieval-based skill augmentation. Our code and training skill libraries are available at https://github.com/lulushang999/SkillFM.

Zuming Zhang, Jie He, Yizhe Zhang +1

Nanyang Technological University · University of Edinburgh · Meta

Flow Matching LLM Agent Skill Learning

Sep 30, 2026cs.LG

Wavelet Flow Matching for Time Series

Synthetic time series are increasingly used for data augmentation, privacy-preserving data sharing, and downstream model development, yet faithfully reproducing both multi-scale temporal structure and cross-channel dependencies remains challenging. We study multivariate time-series generation through flow matching in the wavelet domain. By operating on multilevel discrete wavelet coefficients rather than directly in the time domain, the model represents coarse structure and progressively finer details at separate scales. Their naturally different variances further induce an implicit coarse-to-fine generative process without requiring an explicit multi-scale schedule. Since the transform acts independently on each channel, we pair it with a channel-token transformer whose attention directly models cross-channel dependencies. Across seven benchmark datasets and four sequence lengths, our method is best or tied on a majority of dataset-metric combinations, with the largest and most consistent improvements in Context-FID and discriminative score.

Lucas Poinsignon, Jorge da Silva Goncalves, Samuel Ruiperez-Campillo +1

Dept. of Computer Science ETH Zurich, Switzerland

Flow Matching Time Series Generation Flow-Based Generative Modeling

Sep 30, 2026cs.RO

DiFF: Doppler-informed Flow Matching for Human Motion Flow

Perceiving human motion via privacy-preserving 4D millimeter-wave (mmWave) radar is critical for next-generation human-robot interaction (HRI), where point cloud scene flow serves as a foundational motion representation. Yet the extreme sparsity and noise of 4D radar point clouds make non-rigid motion flow estimation severely ill-posed--a challenge that existing rigid-centric methods and prior works fail to adequately address, largely because they neglect the rich Doppler velocity cues inherent in 4D radar. We propose DiFF, a generative framework that marries Doppler-informed motion priors with a Kolmogorov-Arnold Network (KAN)-based conditional flow matching model. At its core, a KAN-attention mechanism enables expressive feature extraction, while a prior-guided generative process harnesses Doppler cues to regularize the ill-posed solution space. Extensive experiments show that DiFF achieves state-of-the-art (SOTA) performance across diverse real-world datasets, reducing 3D endpoint error to the millimeter scale on the mmBody benchmark.

Kai Wang, Mingle Zhao

Flow Matching Point Cloud Learning Millimeter-Wave Radar mmWave Radar Sensing Human-Robot Interaction

Sep 30, 2026cs.LG

Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support

Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely treats ambient-space regularity or data supported exactly on low-dimensional sets. We study linear FM under a noisy latent-generator model, where a low-dimensional Hölder map is perturbed by nondegenerate ambient Gaussian noise, so the target law is full-dimensional despite its latent structure. We construct a spatially regular ReLU velocity class and establish non-asymptotic high-probability approximation and estimation bounds whose leading sample-size exponent is governed by the latent dimension rather than the ambient dimension, with ambient and noise dependence kept explicit. Fixed positive target noise keeps the interpolation nondegenerate over the full time interval. The same spatial regularity propagates the learned velocity error through the transport ODE, yielding a corresponding Wasserstein convergence guarantee. These results show that exact low-dimensional support is not necessary for Flow Matching to retain latent-dimensional statistical behavior.

Lifeng Hao, Shaolin Ji

Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, Shandong, China.

Flow Matching Flow-Based Generative Modeling

Sep 30, 2026cs.RO

Online Evolution Strategy for Flow-Matching VLA Policies via Self-Supervised Trajectory Distribution Optimization

Vision-Language-Action (VLA) models based on generative frameworks, such as Flow Matching, have recently achieved impressive performance in robotic manipulation. Unlike deterministic policies, Flow Matching enables VLA models to learn conditional action trajectory distributions, where latent noise vectors induce different actions under the same task scenario. However, we observe that these distributions are often ill-formed, with successful and failed behaviors coexisting while considerable probability mass remains in unfavorable regions. To this end, we propose Online-ES, an online adaptation framework for Flow Matching VLAs based on Evolution Strategy (ES), which refines the learned action trajectory distribution through interaction feedback. Instead of pruning the latent noise space, our method performs evolutionary exploration directly in the action trajectory space, where diverse trajectories generated by Flow Matching provide candidate solutions for adaptation. By perturbing sampled trajectories and evaluating their execution outcomes, we derive a self-supervised MSE objective that transfers the evolution direction from trajectory space into model parameter space. Mathematically, we prove that the proposed objective provides an unbiased estimator of the optimal evolution direction. Moreover, we also incorporate failure experiences as negative feedback to regularize the evolution direction, steering the policy away from previously explored failure regions. Experiments in both simulation and real-world environments demonstrate that Online-ES achieves policy improvement comparable to reinforcement fine-tuning, without learning a value model or computing advantages.

Gongxin Yao, Yongsheng Zhao, Jiayin Deng +4

China Mobile (Hangzhou) Information Technology Co., Ltd., Hangzhou, 311121, China

Flow Matching Evolution Strategies Robotic Manipulation Vision-Language-Action Models Test-Time Adaptation of VLA Models

Sep 29, 2026cs.LG

Multi-Agent Flow Matching with Decoupled Generative Guidance

Generative modeling is widely used for producing diverse objects from complex, multimodal distributions. However, its expressivity does not, in general, come with formal guarantees that the generated objects satisfy hard constraints or requirements. In multi-agent generation, this problem becomes more challenging because a hard requirement can depend on multiple agents, while each agent may need to determine its own guidance input without relying on the simultaneously computed guidance inputs of other agents. To this end, we introduce DeGG-Flow, a general framework for multi-agent flow matching with decoupled generative guidance. By representing the generative process as a control-affine dynamical system, we develop guidance conditions for two classes of coupled requirements: shared requirements whose satisfaction depends on multiple agents together, and private requirements associated with each individual agent dependent on its neighbors. For both classes, we establish feasibility conditions and finite-horizon convergence guarantees. We further derive a Wasserstein bound that characterizes the distributional deviation induced by the guidance. We demonstrate DeGG-Flow on multi-robot collaboration for crossing a spatial gap by reconfiguring the environment, and on multi-object scene generation with affordance requirements. Across both applications, DeGG-Flow directly generates objects that satisfy all corresponding hard requirements, including at team sizes unseen during training.

Ruoyu Lin, Magnus Egerstedt, Fabio Pasqualetti

Department of Electrical Engineering and Computer Science, University of California, Irvine, Irvine, CA 92697 USA · University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 USA

Constrained Generative Modeling Flow Matching Multi-Agent Collaboration Multi-Robot Coordination Flow-Based Generative Modeling

Sep 29, 2026cs.AI

MeanFlowAdvantage: Stable Reward Fine-Tuning for Few-Step Average-Velocity Generators

MeanFlow enables efficient few-step generation by predicting interval-average velocities, but this representation creates a mismatch for reward fine-tuning: existing advantage-based objectives are typically defined on instantaneous velocities or equivalent

x_0

-space predictions, whereas inference directly uses the learned average-velocity map. We introduce MeanFlowAdvantage, a signed advantage-weighted least-squares objective for average-velocity generators. Our key construction uses a shared, detached MeanFlow derivative correction to express the reward objective in prediction space while making rollout and reference regularization exact penalties on the average-velocity network deployed at inference. The resulting formulation preserves MeanFlow's native few-step sampler and provides a direct mechanism for transferring reward improvements to the deployed flow map. On SD3.5-Medium, MeanFlowAdvantage improves all eight reported metrics over the matched four-step MeanFlowNFT baseline and, with only four NFEs, matches or exceeds the 40-step DiffusionNFT baseline on six of eight metrics. The same objective also transfers to DNA promoter design, where it supports both teacher-free on-policy RL for a generator defined on a manifold and teacher-guided reward-graded distillation, with the latter yielding the lowest one-step Sei profile MSE among the compared configurations.

Haocheng Tang, Tianchi Xie, Xingqiao Lin

Northeastern University Boston, MA 02115, USA · Tsinghua University Beijing, 100084, PRC · Carnegie Mellon University Pittsburgh, PA 15213, USA

Flow Matching MeanFlow Few-Step Diffusion Sampling Diffusion Model Fine-Tuning Flow Map Learning RL for Diffusion Models+1

Sep 29, 2026cs.RO

PreferenceFlow: Test-Time Guidance of Flow-Matching Robot Policies from Human Interventions

Flow-matching policies can represent complex robot behaviors but remain susceptible to local errors under distribution shift at deployment. Many reinforcement learning approaches to policy improvement require reward signals that are difficult to specify or obtain in real-world manipulation. We present PreferenceFlow, a framework for improving a pretrained flow policy at test time without environment rewards or updates to the base policy. Human intervention chunks are paired with robot chunks generated from the same initial conditioning state to train a preference model. During infer- ence, we adopt the QGF sampling update, replacing its value gradient with the preference gradient evaluated at an estimated clean action. A gradient-cap loss penalizes excessive gradients on intervention pairs, while a zero-gradient loss discourages guidance near actions from expert demonstrations. On four real-world precision insertion tasks with a Franka robot, Pref- erenceFlow achieves a mean success rate of 90.5%, compared with 69% for the frozen policy. Ablations support the roles of gradient regularization and correctly ordered preference labels in the evaluated settings. These results demonstrate the utility of human interventions as local preference supervision for guiding frozen generative robot policies.

Yiqi Tang, Diyuan Shi, Runze Li +1

Westlake University

Flow Matching Robot Policy Learning Human Preference Modeling Robotic Manipulation

Sep 28, 2026cs.CV

Representation by Design in Generation: Cross-View Class-Token Alignment in Diffusion Transformers

Generative and representation learning remain asymmetrically connected: semantic representations are used to improve diffusion generation, whereas the models' own representations are often treated as a by-product of synthesis. We ask whether diffusion models can instead be trained to learn substantially stronger semantic representations without sacrificing generation quality. SelfFlow takes a step in this direction by introducing self-supervised patch alignment into flow matching, but its main gains remain in faster convergence and improved generation. Inspired by DINO and iBOT, we extend this framework with cross-view class-token alignment to further strengthen semantic representations. Specifically, we form two independently noised, dual-timestep observations of each image and align each student class-token representation with the stop-gradient EMA-teacher target from the other observation. This objective is optimized jointly with the inherited flow-matching and local patch objectives. Notably, although the additional objective acts only on the class token, it strengthens both class-token and patch representations. Compared with a matched two-view baseline, ImageNet linear-probing accuracy improves by 9.4% using the class token and 10.1% using mean-pooled patch tokens, while frozen-backbone VOC2012 segmentation improves by 3.6 mIoU. These representation gains are achieved while maintaining comparable ImageNet generation FID. In text-to-image training, the same objective also improves generation FID, reducing it from 2.52 to 2.37 at matched checkpoints. Our results show that representation need not remain a by-product of generation or merely a tool for improving it: it can be directly optimized as a first-class capability of diffusion pretraining alongside generation.

Xiaoyu Wu, Yifei Wang, Chen Wei

Carnegie Mellon University · Rice University

Flow Matching Diffusion Transformer Diffusion-Based Image Generation Self-Supervised Visual Representation Learning

Sep 28, 2026cs.SD

Distill Locally, Schedule Globally: Flow Maps for Few-Step Text-to-Speech

Flow-matching text-to-speech (TTS) models achieve high synthesis quality but require many neural function evaluations (NFEs) to integrate their generative trajectories. Recent few-step flow-map distillation approaches for TTS construct targets from numerically integrated teacher trajectories, creating a trade-off between target accuracy and training cost. We propose Local Flow-Map Distillation (LFMD), which adapts Eulerian Map Distillation to conditional TTS and avoids teacher trajectory integration during target construction. For inference, we derive a sampling schedule (TD-DP) from teacher dynamics and consistency of the learned maps, with a single cost graph supporting multiple NFE budgets without external audio-metric evaluation. Because scheduling offers no flexibility at one NFE, we refine this regime with alignment-aware temporal self-distillation using soft-DTW. Across Seed-TTS and LibriSpeech-PC, LFMD improves low-NFE synthesis over a matched integral-distillation baseline. On Seed-TTS, the refined student reaches 1.80% WER with 1-NFE, compared with 1.76% for its 32-NFE teacher.

Yentl Collin, Evan Dufraisse, Amr Mohamed +3

Institute of Foundation Models (IFM), MBZUAI

Flow Matching TTS Synthesis Generative Modeling Flow-Based Generative Modeling

Sep 28, 2026cs.RO

Rethinking Causal Action Tokenization with Conditional Annealing in Flow Matching

Autoregressive Vision-Language-Action (VLA) models offer a scalable path to robot learning, yet existing action tokenizers treat tokenization as a compression problem, producing representations that are semantically misaligned with the autoregressive backbone. We propose CATok, a causal action tokenizer that reframes tokenization as a causally structured generative process. CATok introduces a conditional annealing mechanism that extracts action tokens by progressively annealing a flow-matching process: each token is conditioned on all preceding tokens and encodes the residual reconstruction signal at a specific noise level, establishing a coarse-to-fine causal token space whose generative semantics are structurally aligned with autoregressive modeling. A token-conditioned flow-matching decoder built on Multimodal Diffusion Transformer (MMDiT) reconstructs continuous action chunks from these discrete tokens with the precision of hybrid diffusion-head architectures. This discrete bottleneck enforces knowledge insulation by design, cleanly separating high-level semantic reasoning from low-level motor execution without requiring explicit attention masking. Extensive evaluations across three simulation benchmarks and real-world robotic manipulation tasks demonstrate that CATok consistently surpasses existing tokenization methods in both reconstruction fidelity-compression tradeoff and inference efficiency, while improving VLA task success rate and training efficiency, establishing a high-performance, scalable foundation for purely autoregressive VLA systems.

Chenyu Zhang, Yuhang Cao, Daru Du +8

IIIS, Tsinghua University · Shanghai Qizhi Institute

Flow Matching Vision-Language-Action Models

Sep 28, 2026cs.LG

Manifold-Stable Flow Matching

Flow matching (FM) learns generative dynamics through velocity regression. Geometric FM variants commonly assume a prior supported on the data manifold, requiring geometric knowledge that is often unavailable. Without such knowledge, low regression error alone does not guarantee manifold adherence. Adherence keeps generated samples within valid configurations and is empirically associated with better task performance. We introduce manifold-stable flow matching (MSFM), which can start from an arbitrary ambient prior, not necessarily supported on the manifold. Using tools from nonlinear dynamics, namely contraction theory, MSFM combines learned tangential transport with prescribed normal contraction. The construction uses analytical projectors for known manifolds and local affine proxies estimated by principal component analysis for unknown data geometry. By implementing contraction theory in both cases of known and unknown manifolds, we guarantee manifold invariance and transverse convergence to the manifold within a desired time window (e.g., one second). We derive a family of compatible probability paths and decompose the training loss into a learnable tangential term and a normal residual. An ellipse experiment attains a mean terminal off-manifold error of order

10^{-6}

. In Push-T robotic experiments, MSFM raises success from

74\%

to

82\%

. In the Robomimic Square task, success increases from

60\%

to

72\%

, while rotation-manifold deviation decreases from order

10^{-2}

to

10^{-7}

. The MSFM terminal geometric errors are controlled by the chosen numerical tolerance. These results demonstrate stronger geometric adherence and higher observed task performance, supporting prescribed normal contraction as a complement to learned generative transport.

Amirhossein Nazerian, Ali Pezeshki, Jianguo Zhao

Department of Mechanical Engineering Colorado State University Fort Collins, CO 80523, USA · Department of Electrical and Computer Engineering Colorado State University Fort Collins, CO 80523, USA

Constrained Generative Modeling Flow Matching Flow-Based Generative Modeling

Sep 28, 2026cs.CV

FILIGREE3D: Scaling Sparse Latent Flow Matching for Ultra-High-Resolution Image-to-3D Generation

Scaling image-to-3D generation to ultra-high resolutions requires controlling rapidly growing computational costs without sacrificing fine geometric detail. We present \textbf{Filigree3D}, a sparse latent flow-matching framework that generates 3D geometry from a single image at voxel resolutions up to

2048^3

, with straightforward extensibility to

4096^3

. To make training tractable, we introduce Structure-Aware Sparse Scaling, which combines spatial bounding with alternating local-global attention to constrain token growth while preserving both fine-scale details and long-range structural context. To enhance detail reconstruction, we curate training samples based on their high-resolution geometric gains and inject multi-scale image features into a sparse 3D DiT, effectively coupling structural semantics with fine-grained visual cues. Furthermore, a visibility-aware voxel regularization strategy improves robustness against sparse perturbations and facilitates the completion of unobserved geometry. Under our default configuration, Filigree3D maintains peak GPU memory consumption within practical limits for contemporary hardware, enabling the generation of highly intricate 3D geometry in approximately one minute. Extensive experiments demonstrate that our method yields substantial improvements in overall geometric fidelity and fine-detail preservation compared to existing baselines, validating practical, detail-preserving 3D generation at unprecedented resolutions.

Hongjie Li, Xinran Yang, Xiuchao Wu +2

AlibabaGroup

Flow Matching 3D ViTs 3D Shape Generation Single-View 3D Reconstruction

Sep 28, 2026stat.ML

Probabilistic Geodesic Flow Matching on Location-Scale Families

Flow matching (FM) has recently emerged as a promising framework for generative modeling due to its conceptual simplicity and strong empirical performance. In FM, samples are transported along a vector field parameterized by a neural network, inducing a probability path that evolves from a simple noise distribution to the target data distribution, governed by an ordinary differential equation (ODE). However, existing FM approaches predominantly rely on probability paths derived from optimal transport (OT) between Gaussian distributions, which may be suboptimal for capturing complex data with inhomogeneous structures such as heavy tail or sharp contrast. In this work, we generalize FM to the broader class of location-scale families for handling data inhomogeneity and introduce a novel class of probability paths defined as geodesics on the manifold of probability distributions. We name this approach probabilistic geodesic flow matching to distinguish it from prior geodesic (Riemannian) FM methods defined in input space. We argue that Euclidean OT-based paths are not necessarily optimal in probability space and may limit modeling flexibility. Through synthetic benchmarks and scientific datasets at different scales, we demonstrate that the proposed method more effectively captures complex distributions, leading to improved or comparable performance compared with SOTA geometry-motivated generative models.

Zeyuan Yu, Zhi Chang, Shiwei Lan

School of Mathematical & Statistical Sciences Arizona State University Tempe, AZ 85287 USA

Flow Matching Generative Modeling Flow-Based Generative Modeling

Sep 28, 2026cs.LG

QAMM: Adjoint MeanFlow Matching for Few-Step Offline Reinforcement Learning

Flow policies can model rich action distributions, but their iterative sampling limits decision speed. Adjoint matching uses the critic's action gradient to improve a flow policy without backpropagating through its sampling trajectory, yet its supervision is defined for instantaneous velocities. We propose QAMM, a method that turns the critic-derived adjoint signal into supervision for MeanFlow's average velocity. The resulting policy learns finite-interval transport directly and generates actions with few network evaluations. We derive the adjoint MeanFlow target, specify its gradient boundaries, and train it with an offline actor-critic. On ten HumanoidMaze tasks, QAMM produces effective two-call policies and achieves competitive performance against strong flow-policy baselines. These results show that adjoint-based Q optimization can be combined with average-velocity learning to obtain expressive offline policies with few-step action generation.

Yuehu Gong, Shutong Ding, Mokai Pan +4

School of Data Science, Fudan University · ShanghaiTech University · Shanghai Innovation Institute

Flow Matching MeanFlow Offline RL Policy Learning

Sep 28, 2026cs.CV

DecFlowEdit: Self-Localized Flow-based Image Editing via Guidance Decoupling

Flow-based image editing (FlowEdit) enables inversion-free semantic changes through the difference between source and target velocities. In this paper, we observe that FlowEdit's default classifier-free guidance (CFG) configuration, with asymmetric source and target scales, causes substantial background leakage. Matching these guidance scales, for example by removing CFG, improves edit-relevant localization but severely degrades editability. To get the best of both worlds, we propose DecFlowEdit, which decouples the optimal guidance scales for localization and for editing in flow-based generative models. In particular, DecFlowEdit first extracts an edit-relevant prior by temporally aggregating velocity differences evaluated without CFG, and then uses this prior to reweight the original updates under default CFG. Our method remains training-free and inversion-free, requiring neither external spatial masks nor attention manipulation. Experiments on PIE-Bench across FLUX, SD3, and SD3.5 show that DecFlowEdit improves background preservation, reducing structure distance by approximately 61 to 73 percent and background LPIPS by 68 to 80 percent relative to FlowEdit at comparable editing fidelity.

Zheyuan Zhan, Can Wang, Jiawei Chen +4

Zhejiang University · University at Buffalo · University of California, Berkeley

Flow Matching Classifier-Free Guidance Text-Guided Image Editing Flow-Based Generative Modeling Image Editing

Sep 28, 2026cs.CV

MotionSpaceFlow: Representation-Aware Flow Matching in Direct Motion Space

Recent advances in diffusion and flow models have substantially improved text-driven human motion generation. Yet most methods generate in low-dimensional, temporally downsampled latent spaces learned primarily for reconstruction, a bottleneck that can limit generation quality and preclude direct manipulation of individual frames and joints. We introduce MotionSpaceFlow (MSFlow), a representation-aware flow-matching framework that predicts clean motion directly in continuous motion space without a learned encoder or decoder. To account for the anisotropic structure of direct motion representations, we propose representation-aware noise scaling and show how the initial Gaussian source scale governs the covariance of intermediate probability-path marginals. We further introduce a Representation-Aware Multimodal Diffusion Transformer (RA-MMDiT), which jointly updates token-level language and full-resolution motion features through joint attention while adapting temporal information flow to the motion representation: causal attention for incremental features defined by frame-to-frame changes, and bidirectional attention for global features such as absolute joint coordinates. Across different datasets and motion representations, MSFlow achieves state-of-the-art text-to-motion performance. Its global representation variant additionally enables zero-shot, inference-time control over any joint or frame through projection sampling without control-conditioned training, delivering leading motion quality with exact constraint satisfaction.

Qing Yu, Kent Fujiwara

LY Corporation, Tokyo, Japan

Flow Matching Text-to-Motion Generation Human Motion Generation Flow-Based Generative Modeling Motion Representation Learning Diffusion Models for Motion Generation

Sep 28, 2026cs.LG

What Does a Stream Model Buy You in Flow Matching?

Stream-level flow matching replaces the linear interpolant of conditional flow matching (CFM) by a Gaussian-process (GP) stream connecting each source--target pair, and reports lower sample error than \icfm{} on 2-Gaussian, MNIST and CIFAR-10 benchmarks. We ask what such a stream model actually contributes. Three results answer the question. (i)\emph{Reduction.} The stream-level CFM objective depends on the stream law only through the per-time joint law of $(s_t,\sdot_t)$ , so the conditional paths a Gaussian stream can reach are exactly the Gaussian conditional paths CFM already parametrises; in the coordinate-wise, shared-scalar-kernel construction gpcfm actually uses, the entire design space collapses to two scalar curves $(m_t,v_t)$ , and cross-time covariance affects only estimator variance. (ii)\emph{The GP is a constrained chart of that space.} One kernel sets both

m_t

and

v_t

, so the paper's own recipe for widening coverage-shrinking the SE length-scale---destroys the interpolant (the midpoint mean weight falls from

1.03

to

0.00

). On the 2-Gaussian benchmark this makes the GP chart diverge on

15/200

runs at high coverage against

0/200

for a decoupled

(m_t,v_t)

chart (

p=6.6\times10^{-5}

), and crossing the two curves shows the divergence tracks the mean, not the variance. On MNIST the same sweep does not diverge and the ordering reverses, so whether the coupling is harmful is benchmark-dependent; what holds on both is that the recipe buys nothing---no coverage level beats the paper's own, and past

\max_t\sqrt{v_t}\approx0.6

both charts degrade. (iii)~\emph{Audit.} The released code does not implement the mechanism it describes: state and velocity are drawn independently (

\mathrm{corr}=0.00\pm0.01

against an intended

\pm0.83

--

0.99

).

Jian Xu

RIKEN

Flow Matching Conditional Flow Matching Gaussian Processes Flow-Based Generative Modeling

Sep 28, 2026cs.CV

SNaP: One-Step Posterior Sampling for Noisy Inverse Problems

Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250

\times

faster than iterative samplers.

Shirin Shoushtari, Edward P. Chandler, Xiao Shi +1

WashU · UW-Madison

Flow Matching MeanFlow Posterior Sampling Accelerated MRI Reconstruction Flow-Based Generative Modeling Diffusion Posterior Sampling+1

Sep 28, 2026cs.LG

FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolution

Long-horizon micromagnetic simulation remains expensive because conventional and learned solvers typically propagate Landau--Lifshitz--Gilbert (LLG) dynamics step by step. Existing learned approaches generally retain stepwise integration or model deterministic evolution, leaving full-field, direct-horizon stochastic prediction largely unexplored. We propose FLARE, a flow-matching framework that recasts stochastic finite-time magnetization prediction as conditional transport over anchor-relative local axis-angle rotations. This rotation-space formulation respects the intrinsic geometry of magnetization dynamics and preserves pointwise unit norm by construction. By explicitly conditioning on the physical prediction horizon, FLARE directly generates full-field stochastic endpoints across multiple target times without stepwise integration. Against the strongest single-checkpoint external baseline on each metric, FLARE achieves 29.9% lower angular energy distance (

15.30^\circ

), and a 37.3% lower fair energy score (0.393). On a representative composed 5-ns two-segment protocol, FLARE achieves a

3{,}062\times

best-batch speedup over the widely used GPU micromagnetic solver MuMax

^3

on a single GPU.

Pengyu Li, Renjie Tong, Xuanlue Jiang +2

State Key Laboratory of Quantum Functional Materials, Department of Physics, and Guangdong Basic Research Center of Excellence for Quantum Science, Southern University of Science and Technology, Shenzhen 518055, China

Sep 27, 2026cs.RO

MomWorld: Momentum-Aware Latent World Model for Long-Horizon Autonomous Driving

Long-horizon planning enables autonomous vehicles to anticipate scene evolution and potential risks, supporting safe and stable decisions in complex interactions. However, existing methods struggle to propagate motion trends from observed history into the future. Long rollouts based on a single latent state may further attenuate useful dynamics, retain stale motion patterns, and disrupt reliable near-term plans. We introduce MomWorld, a momentum-aware latent world model for long-horizon planning. MomWorld extracts scene motion trends from historical-to-current observations and propagates latent momentum into future horizons, jointly predicting future configuration and momentum states. A learnable momentum persistence mechanism preserves stable trends, scene-conditioned momentum updates adapt future dynamics, and a scene-adaptive reset gate suppresses stale momentum under abrupt changes. We further propose MoFlow, a momentum-conditioned flow-matching module that refines a base trajectory to align with the predicted future scene evolution in only a few integration steps, with a horizon-aware residual fusion that preserves near-term planning stability while permitting stronger long-range corrections. Extensive experiments on NAVSIM, nuScenes and Bench2Drive demonstrate that MomWorld improves long-horizon planning consistency and reduces the average collision rate by 12.2% relative to MomAD over a 6-second planning horizon.

Ziying Song, Shengkai Zhang, Lei Yang +6

Nanyang Technological University · Beijing Jiaotong University · North University of China +2

Flow Matching World Model-Based Planning Long-Horizon Planning World Models for Autonomous Driving Latent World Models Autonomous Driving Planning

Sep 27, 2026cs.LG

Source Anchoring for Physical Consistency in Flow Matching Models

Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.

Giulia Romoli, Filippo Ruffini, Paolo Soda

Department of Diagnostics and Intervention, Ume˚a University, Sweden · Unit of Artificial Intelligence and Computer Systems, Universit`a Campus Bio-Medico di Roma, Italy

Constrained Generative Modeling Physics-Informed Generative Modeling Flow Matching Generative Modeling Flow-Based Generative Modeling

Sep 27, 2026cs.AI

Naturalness-guided Manifold Flow Matching for Sign Language Production

Sign Language Production (SLP) aims to generate sign motions from text. Conditional Flow Matching methods have achieved strong performance in SLP by constructing conditional paths that transform a source distribution into a target distribution. However, existing methods construct these paths via linear interpolation, whereas the rotational geometry of human joints confines valid joint rotations to a manifold embedded in Euclidean space. Consequently, linear interpolation between two sign motions leaves this manifold and ignores the motion distribution on it. In this paper, we revisit SLP from the perspective of manifold transport and propose a Naturalness-guided Manifold Flow Matching framework, termed \textbf{SignNMFlow}, which constructs conditional paths directly on the motion manifold by jointly considering geometric efficiency and the motion distribution. Specifically, we exploit the intrinsic geometry of the manifold and introduce a motion naturalness measure to characterize the motion distribution. By minimizing the kinetic energy under this measure, we learn a naturalness-guided interpolation that couples a closed-form geodesic, which provides geometrically efficient transport, with a learnable deviation that incorporates the motion distribution, thereby significantly improving the fidelity of generated sign motions. Extensive qualitative and quantitative evaluations demonstrate the effectiveness of this work.

Jiayi He, Shengeng Tang, Sisi You +3

Hefei University of Technology

Flow Matching Human Motion Generation Riemannian Flow Matching Sign Language Generation

Sep 27, 2026cs.AI

ChronoFlow: Hierarchical Flow Matching for Irregular Time Series Generation

Recent advances in generative modeling have substantially improved time series generation, yet most existing methods either assume a regular temporal grid or focus on feature dynamics under a given sampling structure. This makes them illsuited for generating irregular time series in their native form, where a model must capture not only feature values, but also how many observations occur, when they occur, and which features are observed together. To address this heterogeneous generation problem, we propose ChronoFlow, a unified hierarchical flow matching framework organized by statistical granularity. Following a coarse-to-fine hierarchy, ChronoFlow first generates observation counts and feature-wise frequencies, then jointly generates observation times and feature co-observation patterns, and finally generates values conditioned on the realized pattern. This turns a complex joint generation problem into structurally aligned subproblems while preserving their dependencies. To evaluate complete irregular time series generation, we introduce complementary metrics spanning sample realism, sampling structure, value fidelity, and temporal and cross-feature dependencies, and validate them through controlled corruptions. Across five benchmarks, ChronoFlow achieves strong improvements in generation fidelity over existing baselines, while factorization studies support the proposed hierarchy. Our code is available at https://anonymous.4open.science/r/ChronoFlow.

Changhun Kim, Sunguk Jang, Jeongjun Lee +5

University of Wisconsin–Madison · AITRICS · KAIST

Irregular Time-Series Modeling Flow Matching Time Series Generation Flow-Based Generative Modeling

Sep 24, 2026eess.SP

Structured Pose-Conditioned Flow Matching for Generative 5G CSI Augmentation

With the growing demand for privacy-preserving and occlusion-resilient human pose recognition (HPR), 5G channel state information (CSI) offers a promising contactless sensing modality by integrating communication and sensing capabilities. However, collecting large-scale synchronized CSI-pose pairs remains costly in practical 5G systems. To address this limitation, we propose StructFlow-HPR, a structured pose-conditioned flow matching framework for generative CSI augmentation. StructFlow-HPR learns a continuous latent transport process from Gaussian noise to real CSI representations under pose guidance, while preserving the receiver-frequency topology of CSI through a reconstruction-preserving autoencoder. A pose-conditioned Transformer is further designed to model the latent velocity field and generate pose-aligned CSI samples via ordinary differential equation sampling. Experiments on real-world 5G sensing data show that StructFlow-HPR can produce realistic CSI-pose pairs and improve downstream HPR performance under limited-data conditions.

Haojin Li, Anbang Zhang, Wai Ho Mow +3

University of Science and Technology Beijing, China · Department of ECE, The Hong Kong University of Science and Technology, Hong Kong · University of Exeter +1

Flow Matching Synthetic Data Augmentation Human Pose Estimation Conditional Generative Modeling

Sep 24, 2026cs.CV

Learning a Flow to Self-Supervised Representations

Explicit geometric references offer a direct way to structure self-supervised representations. Existing adversarial distribution-matching formulations, however, require costly encoder-critic optimization. We introduce Flow-Based Distribution Matching (FBDM), a non-adversarial framework that learns this reference-directed geometry through spherical conditional velocity regression. An ETF-inspired reference allows its number of components K' to exceed the auxiliary flow dimension d* while retaining structured geometric separation. We assign both augmented views of each image to the same target, while limiting how many images each reference center can receive. An explicit alignment loss further pulls the two views' representations closer together. Experiments across benchmarks ranging from CIFAR to ImageNet show that FBDM achieves performance nearly on par with DM and remains competitive with existing SSL methods. Matched training-cost comparisons show a 1.48- to 1.83-fold speedup over DM with a negligible increase in GPU memory usage. We also provide a theoretical explanation for the usefulness of the learned representations: under stated conditions, we bound the downstream misclassification rate in terms of the FBDM pretraining loss.

Yuling Jiao, Wensen Ma, Houduo Qi +1

School of Artificial Intelligence, National Center for Applied Mathematics in Hubei, Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, China. · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China. · Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China.

Flow Matching Representation Learning Geometric Representation Learning Self-Supervised Visual Representation Learning

Sep 24, 2026cs.SD

Off-manifold robustness in synthesizer inversion with joint distribution flow matching

Recent work on synthesizer inversion shows that generative models outperform deterministic approaches by explicitly modeling the ambiguity in mapping audio to parameters. Training such models, however, requires audio-parameter pairs, which are typically obtained by rendering sampled or preset parameters through the synthesizer itself. This creates a train-test mismatch that can degrade performance on off-manifold real-world recordings, for which ground-truth parameter annotations do not exist. To circumvent this obstacle, we propose to model the joint distribution of audio and parameters with a multi-modal continuous normalizing flow using independent noise schedules for each modality. This formulation allows us to train joint and conditional densities with paired synthesizer data, while unpaired real recordings can train the audio marginal alone, exposing the model to off-manifold signals without requiring parameter labels. Further, because the model learns to map from audio to parameters at all noise levels, we find that partially noising the audio reference at inference improves real-audio reconstruction, consistent with reducing sensitivity to distribution-specific detail while preserving coarse structure. Evaluating on Surge XT and Dexed, we find that modelling the joint distribution substantially improves both inversion of real-world and in-domain audio.

Ben Hayes

Sony Computer Science Laboratories Paris

Synthetic-to-Real Domain Adaptation Flow Matching Continuous Normalizing Flows

Sep 24, 2026cs.SD

ReaFlow-TTS: Realization-Conditioned Flow Matching for High-Quality and Controllable Speech Synthesis

In flow-matching text-to-speech (TTS), different speech realizations can induce different target velocities under the same generation conditions. A deterministic velocity field trained with squared error predicts their conditional mean, thereby marginalizing realization-dependent variation. Meanwhile, modeling such variation does not inherently provide a semantically interpretable interface for attribute manipulation. We propose ReaFlow-TTS, a realization-conditioned flow-matching framework that introduces an utterance-level stochastic realization latent and uses it to condition velocity prediction throughout the generation trajectory. We further impose valence-arousal-dominance (VAD) semantics on the realization space, enabling direct and graded attribute manipulation without target speech at inference. Experiments demonstrate improved synthesis quality over a matched full-mask baseline and reproducible latent-induced pitch, energy, and timing tendencies across initial-noise samples, providing behavioral evidence that the latent is used as a reusable realization condition. Subjective evaluation further demonstrates graded VAD manipulation across generation contexts with only modest changes in naturalness.

Junyi Zhao, Yihao Qin, Changsheng Ma

School of Information Science and Technology, Lanzhou University, China

Flow Matching TTS Synthesis Controllable Speech Generation Flow-Based Generative Modeling Emotional Speech Synthesis

Sep 23, 2026cs.CV

On the Diffusibility of High-Dimensional Latents

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 (

\boldsymbol{x}_{0}

-prediction) instead, which focuses learning on the underlying signal manifold. Across experiments with multiple strong-reconstruction encoders, we show that

\boldsymbol{x}_{0}

-prediction consistently improves text-to-image generation performance.

Chao Feng, Zhiyang Xu, Bowei Chen +7

Cornell University · Virginia Tech · University of Washington +2

Flow Matching Latent Diffusion Models Autoencoders T2I Generation Flow-Based Generative Modeling Diffusion Models