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

Jul 27, 2026cs.LG

Joint Flow Matching for Generator-Consistent Classification

We introduce Joint Flow Matching (JFM), a training framework for continuous normalising flows over multiple variables. Standard flow matching transports variables from noise to data simultaneously, offering no natural mechanism for forward and reverse conditional inference from a shared joint model. JFM resolves this by assigning opposite roles to each variable at the temporal endpoints. We prove that JFM produces a consistent joint distribution where that forward or reverse integration are conditionals of the same joint. We explore this consistency in the context of joint classification and generation as the basis for interpretability in discriminative-generative models. We validate JFM on conditional datasets producing competitive accuracy with inherently well-calibrated confidence scores without post-hoc calibration, and classifier-consistent image generation.

Hayden McAlister, Lech Szymanski

School of Computing University of Otago Dunedin, New Zealand

Flow Matching Continuous Normalizing Flows Flow-Based Generative Modeling Conditional Generative Modeling

Jul 26, 2026cs.IR

Escaping the Euclidean Void: Manifold-Informed Flow Matching for Sequential Recommendation

Conventional recommenders capture users' preferences by optimizing observed user-item relations, whereas continuous generative recommendation additionally learns the trajectory of synthesizing a target item. Flow matching drives this process by gradually shaping initial noise into a definitive next-item representation through intermediate states in a continuous embedding space. However, item catalogs are discrete and sparsely supported, meaning even a straight Euclidean path can cross continuous regions that contain little evidence of valid item semantics. Formalizing this failure as the Euclidean void, we propose MIRAGE, a Manifold-Informed Rectification framework for Accelerated Generation of Embeddings in sequential recommendation, which rectifies the learned embedding geometry around an unchanged straight probability path. By leveraging an item co-occurrence graph as a proxy for the underlying semantic manifold, MIRAGE aligns interpolated path states with local anchors, reorganizing the embedding space to ground the trajectory in valid item support. MIRAGE retains the original probability path and uses the graph only during training, thereby enabling accurate and efficient one-step inference. Extensive experiments on four real-world datasets reveal that MIRAGE consistently outperforms state-of-the-art baselines, effectively boosting performance on sparsely observed targets while achieving robust overall accuracy. Our code will be made publicly available upon publication.

Dengzhao Fang, Jingtong Gao, Yu Li +2

Jilin University · City University of Hong Kong

Flow Matching Sequential Recommendation One-Step Generative Modeling Manifold Learning Generative Recommendation

Jul 26, 2026cs.LG

Restoration Flow Matching-Based Channel Refinement and Equalization Correction for MIMO Semantic Communications

In multiple-input multiple-output (MIMO) semantic communication, imperfect channel state information (CSI) and equalization mismatch can seriously degrade semantic reconstruction quality. To address this issue, we propose a unified restoration flow matching (RFM)-based framework for channel refinement and equalization correction. Specifically, the channel RFM (CRFM) module is developed to refine the coarse channel, thereby improving channel estimation accuracy. Based on the refined channel, the developed semantic RFM (SRFM) module is employed to correct the residual distortions in the post-equalization latent space. The key idea is to formulate the two cascaded inverse problems of channel estimation and equalization as the unified conditional restoration task, in which the learned conditional velocity field guides the perturbed distribution towards the target distribution. To enhance the robustness of these two modules under various distortion conditions, we develop a dual-anchor perturbation training strategy that jointly learns near-manifold refinement and large-error correction, and implement inference through a few-step deterministic ordinary differential equation (ODE) solver. Extensive experiments on MIMO channels and visual semantic transmission tasks demonstrate that the proposed scheme improves key metrics for channel estimation and semantic reconstruction quality. Moreover, compared with representative diffusion-based generative baselines, the proposed method requires fewer sampling steps.

Wenkai Liu, Nan Ma, Jianqiao Chen +3

State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China · ZGC Institute of Ubiquitous-X Innovation and Applications, Beijing 100876, China · Cooperative Medianet Innovation Center (CMIC) and the Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Flow Matching Semantic Communication Channel Estimation

Jul 25, 2026stat.ML

Logit-Coordinate Generative Models for Mixed Continuous-Categorical Tabular Data

Mixed continuous--categorical data pose a representation problem for continuous generative models. Flow Matching and Gaussian diffusion operate in Euclidean spaces, whereas categorical laws lie on probability simplices and may be highly imbalanced. We study a logit-coordinate framework that encodes categorical variables as smoothed natural parameters and combines them with transformed numerical variables. This yields common formulations of Logit Flow Matching and Logit Diffusion. We introduce a mixed-distribution discrepancy separating categorical marginal error from conditional continuous Wasserstein error, and derive stability bounds and imbalance-aware nonparametric rates linking vector-field or drift error to decoded mixed-distribution error. Controlled simulations show that scaled-logit coordinates improve or match one-hot coordinates, especially under severe rare-cell imbalance. Across four real-data benchmarks and ten splits per dataset, Logit FM improves the primary distributional metrics on three datasets and is comparable on Churn2; Block-Conditional Logit FM consistently improves the flat model; and Logit Diffusion generally improves over or matches One-Hot Diffusion.

Yuefei Shen, Xiaotong Shen

School of Statistics, University of Minnesota

Flow Matching Synthetic Tabular Data Generation Generative Modeling Diffusion Models

Jul 24, 2026cs.LG

FMOPF: Latent Flow Matching with Constraint-Aware Interaction Priors for AC Optimal Power Flow

AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints and is solved thousands of times daily in electricity market operations. Learning a direct mapping from load conditions to OPF solutions can accelerate this computation, yet with deepening renewable penetration, a single optimal dispatch is no longer sufficient. Operators require a characterization of the distribution of feasible near-optimal solutions for risk quantification, sensitivity analysis, and multi-objective trade-off assessment. Supervised neural networks provide fast point predictions but cannot capture this conditional distribution. Diffusion-based generative models can sample diverse solutions in principle, yet existing methods operating in the raw state space exhibit degraded solution quality and fail to scale beyond medium-sized systems. We identify the root cause as the conflation of two distinct tasks within a single model. Compressing the high-dimensional OPF solution manifold is one task, and learning the conditional mapping from loads to that manifold is another. This paper presents FMOPF, a framework that resolves this conflation by decoupling compression from generation through latent flow matching and by explicitly modeling load-state coupling through a Constraint-Aware Interaction Prior Network. Experiments on four IEEE test systems demonstrate that FMOPF provides the most effective Newton-Raphson warm starts, achieves the lowest tail risk among generative methods, and is the first such method to scale to systems with several hundred buses while preserving full feasibility. Ablation studies confirm that the latent generation pipeline is a necessary condition for physical feasibility and that the interaction prior functions as a late-stage tail-risk controller.

Zhilin Huang

China Southern Power Dispatching and Control Center, China Southern Power Grid

Constrained Generative Modeling Flow Matching Uncertainty Quantification Optimal Power Flow Constrained Optimization Power Systems

Jul 22, 2026cs.CV

STEREOFLOW: Progressive Stereo Matching with StereoDiT and Transition Flow Matching

Stereo matching is a fundamental task in 3D reconstruction. Despite remarkable advances, the prevailing paradigms formulate stereo matching as a deterministic regression problem, collapsing the multimodal distribution modeling into a single-point estimation. This formulation suffers from a regression-to-mean bias, frequently struggling with ambiguous regions. In contrast, we introduce a prior-guided generative framework that integrates deterministic matching regression and generative distribution modeling within a complementary formulation. Built upon this formulation, we introduce StereoFlow through three key components: (i) a two-stage progressive cascade matching network that progressively produces multi-resolution stereo conditions with complementary matching cues; (ii) a pixel diffusion transformer (termed StereoDiT) with a frequency-decoupled architecture for modeling correspondence ambiguity; (iii) a few-step flow matching objective (termed Transition Flow Matching) for efficient optimization. In summary, \textsc{\textbf{StereoFlow}} achieves strong geometric consistency and rich fine-grained details in ill-posed, discontinuous regions and under zero-shot generalization. Extensive experiments demonstrate that the proposed StereoFlow establishes multiple state-of-the-art results across benchmarks, including Scene Flow, KITTI, ETH3D, and Middlebury.

Hao Wang, Haoran Geng, Xiaotong Yang +7

School of Computer Science and Engineering, Beihang University, Beijing 100191, China · Google · State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China +3

Flow Matching Diffusion Transformer Stereo Matching

Jul 21, 2026cs.CV

Latent Riemannian Flow Matching for Geometry-Grounded 3D Foundation Models

Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K, ScanNet++ and ETH3D, our method achieves strong performance against recent scene generation baselines in both per-view appearance and aggregated 3D geometry, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation. The project page can be found

\href{https://lisaweijler.github.io/geometry-grounded-rfm/}{\text{here}}

.

Lisa Weijler, Irene Ballester, Guofeng Mei +2

TU Wien · Fondazione Bruno Kessler · Imperial College London

3D Foundation Models Flow Matching Riemannian Flow Matching 3D Scene Generation Generative Modeling 3D Representation Learning

Jul 21, 2026cs.LG

GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks

Equivariant graph neural networks provide a powerful modeling language for three-dimensional scientific data, but their reuse is often limited by implementations tied to specific tasks, outputs, and training regimes. We present GEqTrain, a configuration-driven framework that separates dataset semantics, model composition, and training objectives. Raw data are mapped to typed node-, edge-, and graph-level fields, while model stacks, losses, and training workflows are assembled declaratively through Hydra configurations. A shared equivariant backbone and training infrastructure can therefore be retargeted to a new task primarily through configuration. We demonstrate this flexibility on three different problems handled within one software stack: coarse-grained-to-atomistic backmapping of biomolecular systems, prediction of NMR chemical shifts in molecular solids, and equivariant generative modeling. Our aim is not to surpass individually optimized task-specific systems, but to show that a shared representation and training infrastructure can achieve competitive accuracy across qualitatively different tasks at the cost of a configuration change. We further introduce GEqDiff, a generative extension based on equivariant flow matching. GEqDiff treats user-defined equivariant fields as first-class generation targets, jointly transporting Cartesian positions and non-scalar node fields spanning representations up to l=3 within a single equivariant flow. We validate this capability on a controlled synthetic benchmark inspired by protein secondary-structure motifs, showing that fields with heterogeneous transformation properties can be reconstructed jointly and with high fidelity. By reducing the software overhead of moving between predictive and generative, scalar and tensorial settings, GEqTrain aims to make equivariant modeling more reproducible, extensible, and reusable.

Daniele Angioletti, Marco Nobile, Vittorio Limongelli

Faculty of Biomedical Sciences, Euler Institute, Universit´a della Svizzera italiana, 6900 Lugano, Switzerland

Flow Matching Generative Modeling Equivariant GNNs Equivariant Representation Learning

Jul 17, 2026hep-ph

Learning Standard Model structure from LHC data with Riemannian flow matching

In this work we demonstrate that a single transformer-based generative model can capture Standard Model structure spanning five decades of invariant mass, from the sub-GeV regime to the TeV continuum, a range that no single Monte Carlo sample covers. To achieve this we design \textsc{ShellFlow}, a Riemannian conditional flow matching model that, given the recorded event composition, generates each particle on its on-shell manifold. Its only physics priors are the on-shell condition and the invariant-mass formula. The model is trained on

\sim 10^{9}

real

pp

collision events from the ATLAS Open Data 13~TeV release and told nothing else. From a single training run, the model learns to reproduce all of the following: intra-particle kinematics, the dilepton resonances (

J/ψ

,

Υ

,

Z

) at their PDG positions, the leptonic Weinberg angle, the

W

and top-quark masses, and inter-particle correlations that enter no training objective. A substantial fraction of the Standard Model is thus learnable directly from recorded collision data.

Midori Kato, Kevin A. Urquía-Calderón, Inar Timiryasov +1

Niels Bohr Institute, University of Copenhagen, Jagtvej 155A, DK-2200, Copenhagen, Denmark

Constrained Generative Modeling Flow Matching Conditional Flow Matching Riemannian Flow Matching High-Energy Physics

Jul 16, 2026cs.CV

TanGO: Training-Free 3D Editing via Tangent-Space Guidance and Optimization

While recent flow-matching 3D generative models (e.g., VecSet) adopt structured representations, their tokens share global context, causing conventional training-free editing to suffer from semantic artifacts such as collapsed preserved regions or incomplete transformations. To address this, we propose TanGO, a training-free framework that enables adaptive per-token steering in the tangent space of generative dynamics. To realize this selective control, we formulate a one-step optimal control rule and determine the strength of each token's control signal using a von Mises-Fisher inspired directional discrepancy derived from the source and target velocity fields. Experiments show that TanGO substantially reduces structural artifacts and achieves state-of-the-art performance, outperforming existing 3D editing baselines. The code is publicly available at https://github.com/siw00-lim/TanGO.

Siwoo Lim, Sunjae Yoon, Gwanhyeong Koo +2

Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea · Chung-Ang University, Seoul, Republic of Korea

Flow Matching 3D Shape Editing Flow-Based Generative Modeling

Jul 16, 2026cs.RO

BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching

In robotic motion planning, equivariance to rigid body transformations is crucial for robust spatial generalization. However, current learning-based planners face a critical dilemma: they either lack inherent equivariance, treating transformed tasks as novel scenarios, or enforce it via computationally expensive specialized architectures that bottleneck real-time inference. To break this trade-off, we propose BridgeFlow, a fast and strictly SE(2)-equivariant generative motion planning framework. Rather than relying on heavy equivariant networks, BridgeFlow achieves exact spatial equivariance via a lightweight task-centric canonicalization module, enabling generalization using standard architectures. To further accelerate inference, we pair a Brownian bridge informative prior with context-aware mini-batch optimal transport. This constructs a straightened vector field that minimizes transport costs and stabilizes training. Furthermore, environmental awareness is explicitly embedded via Classifier-Free Guidance. Evaluations in dense 2D environments and on a 7-DoF Franka manipulator demonstrate that BridgeFlow achieves up to a 15x inference speedup and a 2x higher valid trajectory rate over state-of-the-art diffusion baselines, alongside robust generalization to entirely unseen environments and arbitrary spatial transformations.

Xinzhe Zhou, Xuyang Wang, Xiaoming Duan +1

†All authors are with the School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China.

Flow Matching Motion Planning Robot Motion Planning

Jul 16, 2026cs.RO

Reflex: Real-Time VLA Control through Streaming Inference

Flow matching Vision-Language-Action (VLA) models promise precise continuous control, but their iterative denoising nature introduces fundamental incompatibilities with real-time robotics: global timestep injection invalidates KV-caching, forcing a choice between slow

O(N^2)

re-computation or mathematically incorrect cache reuse. We present \textbf{Reflex}, a framework that enables \textit{real-time streaming inference} for flow matching policies by exploiting the \textit{Timestep-Invariance Property} -- that perception encoders are functionally independent of the denoising loop. Reflex partitions the attention context into static, sliding, and dynamic regions, enabling

O(1)

incremental cache updates while preserving full-batch-equivalent attention outputs for fixed inputs. To ensure stability under continuous high-frequency inference, we introduce \textit{AdaRMSNorm}, an adaptive normalization layer that prevents BFloat16 numerical collapse by gating on flow phase. We further maximize throughput through an \textit{async pipeline} that decouples visual encoding from action generation, combined with \textit{operator fusion} that reduces kernel overhead. On LIBERO and Kinetix benchmarks, Reflex achieves a 2.58

\times

inference speedup and 50Hz stable streaming, reducing reaction latency by up to 54% and enabling efficient deployment without performance degradation.

Yuanchun Guo, Bingyan Liu

School of Computer Science, Beijing University of Posts and Telecommunications, Beijing, China.

Flow Matching KV Caching Efficient VLA Model Inference Vision-Language-Action Models

Jul 16, 2026cs.LG

Trajectory-Aware Flow Matching for Topology Optimisation

Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions. Generative TO offers a route to rapid design exploration, but existing models may rely on adversarial training, long reverse-diffusion sampling, or external guidance to maintain structural feasibility and physical consistency. This study develops a flow matching-based topology optimisation (FMTO) framework for conditional topology generation. Linear FMTO is first formulated as an endpoint-based baseline by interpolating between a Gaussian source field and the BESO reference topology. To introduce mechanically meaningful intermediate states, a trajectory-aware FMTO formulation is proposed, where volume-fraction-indexed BESO states are used to construct the probability path and target velocity field. This incorporates physics-guided optimisation history into generative flow learning without adding inference-time optimisation. A path--velocity mismatch analysis explains why moderate trajectory weighting can improve generation stability, whereas excessive guidance may over-constrain the learned transport. Numerical examples show that FMTO generates diverse topology candidates with improved compliance-related performance, volume-fraction satisfaction, topology fidelity, and substantially fewer sampling steps than a diffusion-based baseline. Under limited training data, trajectory-aware FMTO achieves the best overall performance with a moderate trajectory weight. Studies on trajectory-anchor density and three-dimensional topology generation further demonstrate the influence of path design and the applicability of the proposed framework beyond two-dimensional problems.

Shusheng Xiao, Jinshuai Bai, Hyogu Jeong +3

School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, 4000, QLD, Australia · Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China · State Key Laboratory of Advanced Environmental Technology, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640, China +1

Topology Optimization Flow Matching Flow-Based Generative Modeling

Jul 16, 2026cs.RO

NavCMPO: Critic-Guided MeanFlow Policy Optimization for Adaptive Navigation

End-to-end diffusion-based policies have demonstrated strong performance in mapless visual navigation, but their iterative denoising process introduces substantial inference latency, while behavior cloning limits performance to the quality of expert demonstrations. We present NavCMPO, a two-stage adaptive navigation framework that combines few-step MeanFlow trajectory generation, critic-guided refinement, and reinforcement learning fine-tuning. During pre-training, an obstacle proximity prediction task encourages the visual representation to capture obstacle-aware spatial information. To compensate for the degradation in obstacle avoidance caused by few-step generation, Critic-Guided Trajectory Refinement (CGTR) uses gradients from a critic trained with obstacle-point-cloud supervision to refine intermediate trajectories. During adaptation, the MeanFlow policy is fine-tuned using Proximal Policy Optimization with behavior-cloning regularization, while the critic is updated to accommodate embodiment-specific observation changes. Under a matched training budget on the InternVLA-N1 benchmark, NavCMPO achieves an average success rate of 74.7%, exceeding the retrained NavDP baseline by 6.4 percentage points, while reducing inference latency from 85,ms to 60,ms. Experiments on a Unitree Go2 further demonstrate effective sim-to-real transfer.

Junjie An, Yi Wu, Xiao Liu +5

Zhejiang University, Hangzhou, China · Shandong University

Flow Matching Robot Policy Adaptation Trajectory Generation MeanFlow Robot Navigation Diffusion Policy+1

Jul 15, 2026cs.RO

ConFlow: Constraints-Guided Learning with Flow Matching for Motion Generation

In recent years Flow Matching has become a prominent method for generative modeling robot motion generation. In its generic form Flow Matching is an ODE-based neural sampler that is trained by regressing empirical flow fields associated with motion samples as data. However, in robot motion generation we often have additional constraints that might not be present in the collected data. The majority of current approaches train the flow on the available data and use inference-time guidance to enforce task-specific constraints. To address this mismatch, we propose \textbf{ConFlow}, a constraint-guided flow matching framework that incorporates constraint information directly into the training objective via differentiable barrier or cost functions. To address design specifications such as smoothness and boundary conditions, we propose replacing the standard Gaussian source distribution used in flow matching training with a conditional Gaussian Process. Our approach also uses infeasible demonstrations as negative supervision, improving constraint satisfaction without requiring additional expert data. Experiments on a two-robot navigation task demonstrate that ConFlow achieves lower collision rates and higher trajectory quality than standard flow matching baselines, with or without inference-time guidance. These results validate training-time constraint integration as an effective approach to closing the training--inference gap in generative motion models.

Nutan Chen, Jianxiang Feng, Marvin Alles +1

LS Wiiri Robot Innovation Center · Independent Researcher · Technical University of Munich +1

Constrained Generative Modeling Flow Matching Trajectory Generation Robot Motion Generation Flow-Based Generative Modeling

Jul 15, 2026cs.LG

Lyapunov Guidance: A Unified Framework for Stabilizing Generative Flows

Flow matching has emerged as an effective framework for learning complex data distributions, but adapting pretrained flow models to new tasks often requires computationally expensive retraining. Post-training guidance provides a more efficient alternative, but existing methods are largely heuristic and offer no explicit stability guarantees. We address this limitation by proposing LyaGuide, a unified Lyapunov-guided framework that formulates flow guidance as a Lyapunov control problem. Our main theoretical result establishes an equivalence between guided flow matching and Lyapunov control, thereby unifying common guidance strategies, such as classifier guidance, reward guidance, and energy-based guidance, within a single control-theoretic framework. To enforce the Lyapunov condition, we introduce a pseudo-projection operator with a closed-form expression that endows learned or heuristic guidance terms with explicit stability guarantees. LyaGuide supports two practical settings: a model-driven setting, where the target guidance distribution is specified through a known Lyapunov function, and a data-driven setting, where the guidance is adapted from task-specific downstream data. LyaGuide is compatible with existing guidance methods, introduces minimal additional computational overhead, and is straightforward to integrate in practice. Extensive experiments on synthetic benchmarks, image inverse problems, reinforcement learning planning, and energy-based modeling demonstrate consistent improvements in sample quality, guidance fidelity, and robustness, while maintaining computational efficiency.

Jingdong Zhang, Xinze Li, Yize Jiang +3

Department of Mathematics and I-X, Imperial College London, London, United Kingdom · MicroCyto, Beijing, China · Research Institute of Intelligent Complex Systems, Fudan University, Shanghai, China +1

Flow Matching Lyapunov-Based Control Inference-Time Guidance

Jul 15, 2026cs.LG

Heavy-Tailed Flow Matching via Random Clocks

Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes. Standard diffusion and flow-matching models typically begin from Gaussian noise or Gaussian source distributions, which yield tractable training targets but provide a poor inductive match for heavy-tailed data. We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources. Conditioning on a given clock path, the source distribution and flow are Gaussian; marginalizing over the clock gives a Gaussian scale mixture covering Gaussian,

α

-stable, and Student-t families. To make the clock-conditioned vector field practical, we encode the path-valued clock using truncated logsignature features, allowing the velocity field to adapt to the realized conditional space with negligible overhead. Empirically, on 2D imbalanced

α

-stable mixtures, CIFAR10-LT, and HRRR weather fields, HTFM improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and competitive heavy-tailed baselines, while retaining the low-NFE sampling advantage of flow matching. Moreover, the random-clock formulation further provides a practical tail-control interface: by varying only the clock law or tail parameter, the same architecture can calibrate the ``heaviness'' of generated tails across different distribution families.

Zhouhao Yang, Yezhen Wang, Kenji Kawaguchi +2

Department of Applied Mathematics and Statistics, Johns Hopkins University. · School of Computing, National University of Singapore. · Department of Computer Science, Johns Hopkins University.

Flow Matching Heavy-Tailed Noise Generative Modeling Flow-Based Generative Modeling Heavy-Tailed Distributions

Jul 14, 2026cs.CV

RFMSR: Residual Flow Matching for Image Super-Resolution

Image super-resolution (ISR) has witnessed remarkable progress with diffusion models and flow matching. The dominant text-to-image (T2I) based approaches leverage large-scale foundation models as generative priors, achieving impressive perceptual quality but at the cost of massive model sizes and prohibitive training expenses. Recent flow-matching-based vision-only approaches have made significant strides; however, they adopt standard flow formulations that transport from a pure Gaussian prior to the data distribution, discarding the rich structural information already present in the low-quality (LQ) input. Furthermore, existing single-step acceleration techniques often forfeit the model's multi-step inference capability. In this paper, we propose Residual Flow Matching for Image Super-Resolution (RFMSR), a vision-only framework that centers the source distribution at the LQ latent, reducing transport distance and preserving structural priors throughout the flow trajectory. We further introduce a two-phase training strategy: Phase I pretrains the velocity field via conditional flow matching, while Phase II applies end-to-end supervision to the single-step prediction while retaining the velocity loss across all timesteps, achieving high-quality single-step generation without sacrificing multi-step refinement. Extensive experiments demonstrate that RFMSR achieves comparable or even superior perceptual quality compared to state-of-the-art (SOTA) methods. The source code is available at https://github.com/Faze-Hsw/RFMSR.

Shuwei Huang, Tianyao Luo, Jicheng Liu +2

Huazhong University of Science and Technology · Wuhan University

Flow Matching Image Super-Resolution

Jul 14, 2026cs.LG

The Geometry of Memorization: Finite-Time Spectral Sensitivity as a Diagnostic for Flow Matching Models

Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations. This paper presents the Finite-Time Spectral Sensitivity (FTSS) g(t), a gradient-free, forward-pass metric that exposes flow geometry by tracking the root-mean-square singular value of the state-transition matrix. Serving as a continuous proxy for stable rank, g(t) reveals a distinct geometric pathology under data scarcity: while generalizing models maintain stable effective dimensions, overfitting causes a spectral collapse. We leverage this structural phenomenon to develop an internal geometric audit based on g(t). Our framework detects generative memorization using purely internal trajectory dynamics, removing the need for external membership queries or baseline data comparison.

Shuchan Wang

Flow Matching Neural Network Memorization Memorization in Generative Models Generative Modeling Flow-Based Generative Modeling

Jul 14, 2026cs.CV

DiTailed: Ensuring Visual Object Consistency in Text-Image-to-Image Flow Matching Models

Despite remarkable progress in text-guided image editing, generative models frequently fail to preserve visual object consistency, defined as the preservation of a subject's key attributes throughout the editing process. We address this limitation through three contributions. First, we introduce ABO-Edit, a dataset specifically designed to study object consistency, comprising over 12,000 triplets of source images, editing prompts, and high-quality target images rendered from artist-designed 3D assets, with multi-view coverage and human-verified quality control. Second, we uncover an overlooked property of image-editing rectified flow models: the conditioning embedding space, not directly supervised during training, encodes a prediction of the final generated image even at high noise levels. Third, exploiting this finding, we propose FlowMirror, a parameter-free auxiliary loss that supervises this conditioning embedding space. Without architectural changes, our method improves generation quality across several metrics over baselines.

Francesco Taioli, Daniel Coelho, Iaroslav Melekhov +4

Amazon · Faculty

Flow Matching Text-Guided Image Editing Rectified Flow Image Editing

Jul 14, 2026cs.CV

Contrastive-Augmented Flow Matching for Style-Content Disentanglement

Learning representations that separate content and style is crucial for controllable generation and compositional generalization. However, diffusion and flow-based models trained primarily with generative objectives often produce entangled or misaligned factors. To address this gap, we introduce Contrastive Augmented Flow Matching (CAtFM), a framework that integrates contrastive regularization into an invertible flow matching formulation to promote structured content-style representations. Rather than constraining intermediate latents or velocity fields, we apply contrastive supervision to predicted endpoints during training, enforcing semantic consistency across transported distributions while allowing disentanglement to emerge implicitly, without assuming strictly pure or fully factorized content and style representations. Our main experiments operate in the CLIP embedding space, with additional validation using frozen DINO and ALIGN encoders. Across synthetic data, in-domain styles, and real-world benchmarks (ImageNet, WikiArt, DomainNet, and DTD), CAtFM improves content and style retrieval, enhances embedding cluster separation, and achieves stronger open-set robustness compared to generative and discriminative baselines. Overall, CAtFM provides a simple way to couple discriminative constraints with deterministic transport, improving disentanglement and robustness under distribution shift.

Yusong Li, Pingchuan Ma, Ming Gui +2

Computer Vision & Learning Group at the University of Munich

Flow Matching Disentangled Representation Learning Representation Disentanglement

Jul 13, 2026cs.LG

Velocity Scheduled Flow Matching

Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations~(NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout the trajectory. We relax this choice and introduce Velocity Scheduled Flow Matching~(VSFM), which replaces the conditional target

x_1 - x_0

with

v(t)(x_1 - x_0)

for any nonnegative profile

v:[0,1]\to\mathbb{R}_{\geq 0}

satisfying

\int_0^1 v\,dt = 1

. We study six polynomial profiles drawn from motion planning. The first use of VSFM is at inference time: a pretrained linear flow-matching model can be sampled under any admissible profile by integrating its ODE on a non-uniform

τ

-schedule, with no retraining and no additional computation; on CIFAR-10 this lowers FID by up to

19.8\%

. Training from scratch under a braking profile gives a further reduction of

17.4\%

at

4

~NFE. Both gains follow from the local truncation error of the Euler integrator on the induced grid.

Vitalii Bondar

Cherkasy State Technological University Cherkasy, Ukraine

Flow Matching Conditional Flow Matching Few-Step Diffusion Sampling Flow-Based Generative Modeling

Jul 13, 2026cs.CV

FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction

Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.

Zheng Zhang, Hao Tang, Yingying Hu +2

Centre for Smart Health, The Hong Kong Polytechnic University, Hong Kong, China · Department of Nuclear Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China · Research Center for Medical AI, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

Flow Matching Image Reconstruction PET/CT Imaging Physics-Informed ML

Jul 12, 2026cs.GR

LATO.2: Factorized 3D Mesh Generation with Vertex and Topology Flow

Flow matching over carefully designed latent representations has recently emerged as a powerful paradigm for topology-aware mesh generation. Existing approaches, however, model vertices and connectivity jointly in a joint latent space, entangling continuous vertex geometry with discrete combinatorial structure; this complicates flow learning and manifests as drifting vertices and broken surfaces. We present LATO.2, a factorized flow matching framework that decomposes mesh generation into a vertex flow followed by a connectivity flow conditioned on the realized vertices, with both stages anchored to a shared coarse voxel scaffold. Dedicated VAEs underpin the two stages, recovering vertices at sub-voxel precision and embedding discrete connectivity into a continuous latent space. We demonstrate two advantages unique to this factorization: (i) part-wise generation, in which the scaffold is partitioned and each part synthesized at full latent capacity, yielding substantially higher-resolution meshes than a monolithic latent permits; and (ii) topology-adaptive editing, in which manipulating first-stage vertices induces the corresponding connectivity without re-optimization. Experiments show that LATO.2 surpasses state-of-the-art topology-aware mesh generators in geometric fidelity and connectivity quality.

Hang Long, Tianhao Zhao, Junkai Lin +7

Huazhong University of Science and Technology · Meshy AI · Independent Researcher +1

Flow Matching 3D Mesh Generation 3D Shape Generation Discrete Flow Matching

Jul 11, 2026cs.RO

SUREFlow: State-space Uncertainty-aware REsidual Flow Matching for Robust Robot Manipulation

Generative vision-language-action policies have advanced robot manipulation, but they often exhibit instability under noise, partial observability, and stochastic initial conditions. During extended rollouts, small velocity errors accumulate, degrading execution reliability. Existing diffusion and flow-based policies typically assume homoscedastic residuals and lack explicit uncertainty modeling within action generation, limiting robustness during iterative rollout. We propose SUREFlow, a state-space uncertainty-aware residual flow matching framework built on a Mamba backbone. The method jointly predicts action velocities and input-dependent residual uncertainty, enabling selective refinement of unreliable action dimensions without environment feedback while preserving computational efficiency. On LIBERO, SUREFlow achieves 92.5% average success rate (SR), outperforming the Mamba-based MaIL by 34.2%. On LIBERO-PRO, it attains around 49% SR using only 179M parameters, achieving performance comparable to large VLAs with 3-7B parameters. SUREFlow source code is available on: https://github.com/tanvirnwu/SUREFlow

Md Tanvir Islam, Sai Navaneet Peddapalli, Sangmoon Lee +1

School of Electronic and Electrical Engineering, Kyungpook National University, Daegu 41566, Republic of Korea

Flow Matching Uncertainty Estimation for VLA Models Language-Conditioned Robot Manipulation Robustness of VLA Models

Jul 11, 2026eess.AS

FdAudio: MeanFlow-Anchored Fréchet-Distance Post-Training for One-Step Text-to-Audio Generation

While recent few-step sampling text-to-audio generation models like MeanAudio substantially accelerate generation by modeling average velocities, their strict one-step generation quality still lags significantly behind multi-step counterparts. We propose FdAudio to bridge this gap. Unlike MeanAudio, which relies solely on regression against target velocity fields, our post-training approach optimizes the final one-step distribution directly across pre-trained embedding spaces via a multi-representation Fréchet-distance (FD) loss. Crucially, to prevent the multi-step degradation that naive post-training with FD-loss causes, we introduce a MeanFlow consistency objective as a structural anchor. Results demonstrate that FdAudio establishes state-of-the-art one-step T2A generation quality among few-step systems, yielding an 11.4% reduction in FD score and a 28.8% improvement in FAD score relative to the baseline MeanAudio framework. Notably, we solve FD post-training's naive multi-step degradation issue by proposing the MeanFlow anchor, enabling a 25-step sampling path to maintain high-fidelity audio synthesis that matches or surpasses strong multi-step models at a fraction of their computational latency.

Kuan-Po Huang, Bo-Ru Lu, Ho-Lam Chung +2

National Taiwan University · Amazon

Text-to-Audio Generation Flow Matching One-Step Generative Modeling Few-Step Diffusion Sampling Mean Flow

Jul 11, 2026cs.RO

Source-Lifted Flow Matching for Intervenable Multimodal Imitation

Flow-matching policies are promising for imitation learning because they model complex multimodal action distributions. However, their stochasticity is largely passive: repeated sampling may yield diverse behaviors, but users cannot directly choose among valid continuations from the same state. We propose Source-Lifted Flow Matching (SL-FM), a source-intervenable flow-matching policy that exposes such a handle while keeping the velocity field shared and latent-free (without a separate discrete-handle input). The handle selects only the source endpoint of the conditional flow, not a mode-specific field, preserving the standard formulation while avoiding decomposition into separate mode-conditioned dynamics. The core mechanism is Orthogonal Source Lifting, designed to prevent path-crossing ambiguity. Instead of partitioning target actions by mode, SL-FM lifts handle-specific sources into auxiliary orthogonal coordinates and keeps targets in the original action subspace. This preserves the demonstrated action distribution while allowing one shared field to carry different branches without merging at crossings. To keep handles usable across states, we learn a state-dependent source mixture end to end and use a responsibility floor, giving each handle weak supervision and mitigating dead modes. Experiments on crossing-flow diagnostics and robot-control benchmarks show that SL-FM converts passive source randomness into an actionable intervention variable. It removes crossing-induced composite trajectories, changes future routes in 91.1% of matched-prefix interventions, and achieves strong free-deployment performance, with improvements in several benchmark settings. Overall, source geometry provides actionable multimodal control without conditioning the velocity field on the selected mode.

He Zhang, Ying Sun, Ziyang Chen +6

The Hong Kong University of Science and Technology (Guangzhou) · AI2 Robotics

Robotic Control Flow Matching Imitation Learning Robot Imitation Learning

Jul 9, 2026physics.optics

Joint Discrete-Continuous Flow Matching for Open-Vocabulary Inverse Design of Multilayer Optical Coatings

Amortized neural inverse design typically remains closed-world: component choices are fixed vocabulary tokens, coordinate grids are frozen at training time, and continuous variables are discretized into sequence tokens. Multilayer optical coatings are an industrially important instance, coupling material sequence, layer thickness and wavelength-dependent response. We present IrisFlow, a query-based, open-vocabulary flow-matching framework instantiated in coatings: the target reflectance/transmittance spectrum, wavelength grid, candidate-material optical constants and layer count are supplied at query time. Candidate materials enter as wavelength-aware optical tokens rather than learned identities; material sequences are sampled by discrete flow matching over the query's candidate bank, thicknesses by continuous flow matching without discretization. A single 136M-parameter model designs 2-100-layer stacks. Across a 224-task benchmark it reconstructs in-distribution targets faithfully and retains same-order accuracy on a 15-material held-out bank without retraining; it reconstructs bands up to 1100 nm beyond its training envelope, designs against analytic application specifications and outperforms an autoregressive baseline on that baseline's material library. With optical constants calibrated to our deposition process, IrisFlow designs four color-displaying coolers, fabricated by ion-assisted evaporation: the three chromatic devices reach a CIEDE2000 color error of 3.1-5.2 while retaining 93-95% solar near-infrared reflectance, demonstrating open-vocabulary design carried through to fabricated coatings.

Zhiyi Li, Yuheng Jin, Yidan Huang +3

School of Electronic Science and Engineering (National Model Microelectronics College), Xiamen University, Fujian, 361005, China. · 2Fujian Key Laboratory of Ultrafast Laser Technology and Applications, Xiamen University, Xiamen, 361005, China.

Flow Matching Inverse Design Discrete Flow Matching

Jul 8, 2026eess.SP

Stability of Flow Models for Graph Signals

Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation. In this paper, we analyze continuous normalized flow models parameterized by GNNs and show that permutation equivariance is preserved for both the resulting continuous-time ordinary differential equations and their discrete numerical approximations used as graph signal samplers. Our primary contribution is to derive explicit stability bounds on the generated probability distributions, which quantify how relative graph perturbations affect the final sampled signals. Motivated by these theoretical bounds, we introduce a stability-promoting regularized flow matching strategy that actively penalizes the spatial Lipschitz constant of the vector field during model training. Experiments using synthetic smooth signals on stochastic block model graphs and real-world fMRI signals on brain connectomes demonstrate that this bound-oriented approach yields generative models that are more robust to structural noise, without sacrificing output quality.

Martin Schmidt, Gonzalo Mateos

Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA

Graph Signal Processing Flow Matching Continuous Normalizing Flows Equivariant GNNs Flow-Based Generative Modeling

Jul 8, 2026cs.RO

Flow-ERD: Agent-type Aware Flow Matching with Entropy-Regularized Distillation for Diverse Traffic Simulation

Realistic and diverse traffic simulation is essential to autonomous driving development. Yet prevailing benchmarks predominantly reward realism, and recent methods have optimized accordingly, leaving diversity underexplored. We introduce \textbf{Flow-ERD}, a multi-agent simulator that pursues realism and diversity jointly. Its backbone, \textbf{Agent-Type Aware Flow Matching} (AFM), couples flow matching's multi-modal expressiveness with type-specific kinematic execution. It preserves fine-grained diversity while keeping motions consistent with each agent type. A second stage, \textbf{Entropy-Regularized Distillation} (ERD), fine-tunes the closed-loop rollout distribution with an entropy-regularized reverse-KL objective. This mitigates covariate shift while explicitly preventing collapse onto high-density modes. We evaluate Flow-ERD with a log-free diversity metric alongside standard realism scores. Flow-ERD ranks first on the WOSAC test benchmark and dominates the realism--diversity Pareto front among reproducible baselines. Our project page is available here.

Seulbin Hwang, Kiyoung Om, Daejung Kim +1

NAVER LABS Corp., Republic of Korea

Autonomous Driving Benchmarks Flow Matching Intelligent Transportation Systems Autonomous Driving Simulation