Flow Matching

Follow this topic Ask about this topic

Momentum

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

May 7, 2026cs.LG

A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models, score-based generative models, and flow matching are instances of learning a time-dependent vector field that induces a family of marginals

(ρ_t)_{t \in [0,1]}

governed by continuity and Fokker-Planck equations. Such a unified theory is timely because these methods are converging methodologically, yet fragmented notation and competing derivations continue to obscure their shared structure and the practical tradeoffs governing sampling, stability, and computation. Within this framework, we (i) derive reverse-time sampling for diffusion and score-based models as controlled stochastic dynamics, (ii) show that the probability flow ODE yields identical marginals and connects diffusion to likelihood-based normalizing flows, and (iii) interpret flow matching as direct regression of the velocity field under a chosen interpolation, clarifying when it coincides with or differs from score-based training. We compare objectives, sampling schemes, and discretization errors under unified notation, discuss connections to Schrodinger bridges and entropic optimal transport, and summarize theoretical guarantees and open problems on approximation, stability, and scalability.

Aditya Ranganath, Mukesh Singhal

Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore, CA 94551, USA · Department of Electrical Engineering University of California Merced, CA 95343, USA

Flow Matching Generative Modeling Flow-Based Generative Modeling Score-Based Generative Modeling Diffusion Models

May 7, 2026cs.CV

FREPix: Frequency-Heterogeneous Flow Matching for Pixel-Space Image Generation

Pixel-space diffusion has re-emerged as a promising alternative to latent-space generation because it avoids the representation bottleneck introduced by VAEs. Yet most existing methods still treat image generation as a frequency-homogeneous process, overlooking the distinct roles and learning dynamics of low- and high-frequency components. To address this, we propose FREPix, a FREquency-heterogeneous flow matching framework for Pixel-space image generation. FREPix explicitly decomposes generation into low- and high-frequency components, assigns them separate transport paths, predicts them with a factorized network, and trains them with a frequency-aware objective. In this way, coarse-to-fine generation becomes an explicit design principle rather than an implicit behavior. On ImageNet class-to-image generation, FREPix achieves competitive results among pixel-space generation models, reaching 1.91 FID at

256\times256

and 2.38 FID at

512\times512

, with particularly strong behavior in the low-NFE regime.

Mingfeng Lin, Jiakun Chen, Liang Han +1

Harbin Institute of Technology (Shenzhen)

Flow Matching Conditional Image Generation Image Generation Pixel-Space Diffusion Models Flow-Based Generative Modeling

May 7, 2026cs.LG

A Flow Matching Algorithm for Many-Shot Adaptation to Unseen Distributions

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this end, we propose Function Projection for Flow Matching (FP-FM), an algorithm that directly conditions generation on samples from the target distribution. FP-FM learns basis functions to span the velocity fields corresponding to a set of training distributions, and adapts to new distributions by computing a simple least-squares projection onto this basis. This enables efficient generation of samples from diverse target distributions without additional training at inference time. We further introduce multiple variants of FP-FM that provide a trade-off in expressivity and compute by enriching the coefficient calculation, e.g., by making the coefficients dependent on time. FP-FM achieves greatly improved precision and recall relative to baselines across synthetic and image-based datasets, with especially strong gains on unseen distributions.

Tyler Ingebrand, Ruihan Zhao, Kushagra Gupta +3

University of Texas at Austin

Flow Matching Flow-Based Generative Modeling Conditional Generative Modeling

May 7, 2026cs.LG

Entropy-Regularized Adjoint Matching for Offline Reinforcement Learning

Integrating expressive generative policies, such as flow-matching models, into offline reinforcement learning (RL) allows agents to capture complex, multi-modal behaviors. While Q-learning with Adjoint Matching (QAM) stabilizes policy optimization via the continuous adjoint method, it remains inherently bound to the fixed behavior distribution. This dependence induces a \textit{popularity bias} that can suppress high-reward actions in low-density regions, and creates a \textit{support binding} that restricts off-manifold exploration. Existing workarounds, such as appending \textit{residual} Gaussian policies, often re-introduce the expressivity bottlenecks associated with unimodal distributions. In this work, we propose \textit{Maximum Entropy Adjoint Matching} (ME-AM), a unified framework that addresses these limitations within the continuous flow formulation. ME-AM incorporates two mechanisms: (1) a Mirror Descent entropy maximization objective that mitigates the popularity bias to facilitate the extraction of optimal policies from offline datasets, and (2) a \textit{Mixture Behavior Prior} that broadens the geometric support to encompass out-of-distribution high-reward regions. By exploring this extended geometry, ME-AM identifies robust actions while preserving the absolute continuity of the generative vector field. Empirically, ME-AM demonstrates competitive or superior performance compared to prior state-of-the-art (SOTA) methods across a diverse suite of sparse-reward continuous control environments.

Abdelghani Ghanem, Mounir Ghogho

College of Computing Mohammed VI Polytechnic University Rabat 11103, Morocco

Flow Matching Offline RL Maximum Entropy RL

May 7, 2026cs.AI

P-Guide: Parameter-Efficient Prior Steering for Single-Pass CFG Inference

Classifier-Free Guidance (CFG) is essential for high-fidelity conditional generation in flow matching, yet it imposes significant computational overhead by requiring dual forward passes at each sampling step. In this work, we address this bottleneck by introducing \textbf{P-Guide}, a framework that achieves high-quality guidance through a single inference pass by modulating only the initial latent state. We further show that, under a first-order approximation, P-Guide is equivalent to CFG in the sense that it steers generation from the prior space, without requiring explicit velocity field extrapolation during sampling. We consider both homoscedastic and \textbf{heteroscedastic} priors, and find that jointly modeling the mean and variance enables adaptive loss attenuation and improved robustness to data uncertainty. Extensive experiments demonstrate that P-Guide reduces inference latency by approximately 50% while maintaining fidelity and prompt alignment competitive with standard dual-pass CFG baselines.

Xin Peng, Ang Gao

School of Physical Science and Technology, Beijing University of Posts and Telecommunications, Beijing, China

Flow Matching Classifier-Free Guidance Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 7, 2026cs.LG

Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems

Reconstructing high-fidelity flow fields from low-fidelity observations is a central problem in scientific machine learning, yet recent diffusion and flow-matching models typically rely on iterative sampling, making them costly for latency-sensitive workflows such as ensemble forecasting, real-time visualization, and simulation-in-the-loop inference. We study whether a high-fidelity flow-matching generative model can be compressed into a compact one-step model for fast scientific flow reconstruction. Our approach distills an optimal-transport flow-matching teacher into a one-step consistency model. Low-fidelity observations are incorporated at inference by initializing the generative trajectory from a noised observation along the transport path, allowing an unconditional high-fidelity flow model to perform conditional reconstruction without retraining the teacher. We evaluate this distillation strategy on three fluid benchmarks, Smoke Buoyancy, Turbulent Channel Flow, and Kolmogorov Flow, using coarse-to-fine reconstruction as a controlled testbed at field sizes up to

256 \times 256

. Across these settings, the distilled student retains similar performance of the teacher's model on spectrum metrics, while using roughly half as many parameters and achieving a

12\times

inference speedup over the flow-matching teacher. Under the same training budget, the distilled student also outperforms a one-step consistency model trained directly from scratch by

23.1\%

in SSIM, showing that teacher distillation improves training efficiency rather than merely accelerating sampling. These results suggest a promising route for turning future high-capacity scientific generative models into compact reconstruction models that are faster to train, cheaper to run, and easier to deploy.

Sicheng Ma, Tianyue Yang, Xiuzhe Wu +1

Department of Physics University of Cambridge · The Center for Computational Science University College London · Department of Computer Science University College London

Flow Matching One-Step Generative Modeling Consistency Distillation Flow-Based Generative Modeling

May 7, 2026cs.AI

SDFlow: Similarity-Driven Flow Matching for Time Series Generation

Vector quantization (VQ) with autoregressive (AR) token modeling is a widely adopted and highly competitive paradigm for time-series generation. However, such models are fundamentally limited by exposure bias: during inference, errors can accumulate across sequential predictions, leading to pronounced quality degradation in long-horizon generation. To address this, we propose SDFlow (

\textbf{S}

imilarity-

\textbf{D}

riven

\textbf{Flow}

Matching), a non-autoregressive framework that operates entirely in the frozen VQ latent space and enables parallel sequence generation via flow matching. We tackle three key challenges in making this transition: (1) eliminating exposure bias by replacing step-wise token prediction with a global transport map; (2) mitigating the high-dimensionality of VQ token spaces via a low-rank manifold decomposition with a learned anchor prior over the latent manifold; and (3) incorporating discrete supervision into continuous transport dynamics by introducing a categorical posterior over codebook indices within a variational flow-matching formulation. Extensive experiments show that SDFlow achieves state-of-the-art performance, improving Discriminative Score and substantially reducing Context-FID, particularly for challenging long-sequence generation. Moreover, SDFlow provides significant inference speedups over autoregressive baselines, offering both high fidelity and computational efficiency. Code is available at https://anonymous.4open.science/r/SDFlow-D6F3/

Wei Li, Shibo Feng, Pengcheng Wu +3

1Shanghai Jiao Tong University · 2Shanghai University · 3Nanyang Technological University +2

Flow Matching Time Series Generation Flow-Based Generative Modeling

May 7, 2026stat.ML

Spherical Flows for Sampling Categorical Data

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere

\mathbb S^{d-1}

. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on

\mathbb S^{d-1}

to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on

(\mathbb S^{d-1})^L

both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.

Jannis Chemseddine, Gregor Kornhardt, Gabriele Steidl

Technische Universität Berlin

Flow Matching Synthetic Data Generation Generative Modeling Flow-Based Generative Modeling Sequence Modeling

May 6, 2026cs.CV

Direct Product Flow Matching: Decoupling Radial and Angular Dynamics for Few-Shot Adaptation

Recent flow matching (FM) methods improve the few-shot adaptation of vision-language models, by modeling cross-modal alignment as a continuous multi-step flow. In this paper, we argue that existing FM methods are inherently constrained by incompatible geometric priors on pre-trained cross-modal features, resulting in suboptimal adaptation performance. We first analyze these methods from a polar decomposition perspective (i.e., radial and angular sub-manifolds). Under this new geometric view, we identify three overlooked limitations in them: 1) Angular dynamics distortion: The radial-angular coupling induces non-uniform speed on the angular sub-manifold, leading to regression training difficulty and extra truncation errors. 2) Radial dynamics neglect: Feature normalization discards modality confidence, failing to distinguish out-of-distribution and in-distribution data, and abandoning crucial radial dynamics. 3) Context-agnostic unconditional flow: Dataset-specific information loss during pre-trained cross-modal feature extraction remains unrecovered. To resolve these issues, we propose warped product flow matching (WP-FM), a unified Riemannian framework that reformulates alignment on a warped product manifold. Within this framework, we derive direct product flow matching (DP-FM) by introducing a constant-warping metric, which yields a decoupled cylindrical manifold (i.e., direct product manifold). DP-FM enables independent radial evolution and constant-speed angular geodesic transport, effectively eliminating angular dynamics distortion while preserving radial consistency. Meanwhile, we incorporate classifier-free guidance by conditioning the flow on the pre-trained VLMs' hidden states to inject missing dataset-specific information. Extensive results across 11 benchmarks have demonstrated that DP-FM achieves a new state-of-the-art for multi-step few-shot adaptation.

Hongxu Chen, Yanghao Wang, Bowei Zhu +6

HKUST · USTC · Huawei Research

Cross-Modal Learning Flow Matching VLM Adaptation Cross-Modal Alignment

May 6, 2026cs.RO

Conditional Flow-VAE for Safety-Critical Traffic Scenario Generation

Safety-critical scenarios are essential for the development of autonomous vehicles (AVs) but are rare in real-world driving data. While simulation offers a way to generate such scenarios, manually designed test cases lack scalability, and adversarial optimization often produces unrealistic behaviors. In this work, we introduce a conditional latent flow matching approach for scalable and realistic safety-critical scenario generation. Our method uses distribution matching to transform nominal scenes into safety-critical rollouts. Furthermore, we demonstrate that incorporating both simulation and real-world data enables our framework to efficiently generate diverse, data-driven scenarios. Experimental results highlight that our approach is able to more consistently and realistically generate novel safety-critical scenarios, making it a valuable tool for training and benchmarking AV systems.

Zimu Gong, Brian Zhaoning Zhang, Chris Zhang +2

University of Michigan-Ann Arbor · University of Waterloo · 1Waabi Innovation Inc +1

Flow Matching Synthetic Data Generation for Robotics Conditional Variational Autoencoder Autonomous Driving Simulation Autonomous Driving Scenario Generation

May 5, 2026cs.CV

FluxFlow: Conservative Flow-Matching for Astronomical Image Super-Resolution

Ground-to-space astronomical super-resolution requires recovering space-quality images from ground-based observations that are simultaneously limited by pixel sampling resolution and atmospheric seeing, which imposes a stochastic, spatially varying PSF that cannot be resolved through upsampling alone. Existing methods rely on synthetic training pairs that fail to capture real atmospheric statistics and are prone to either over-smoothed reconstructions or hallucination sources with no physical counterpart in the observed sky. We propose FluxFlow, a conservative pixel-space flow-matching framework that incorporates observation uncertainty and source-region importance weights during training, and a training-free Wiener-regularized test-time correction to suppress hallucination sources while preserving recovered detail. We further construct the DESI--HST Dataset, the large-scale real-world benchmark comprising 19,500 real co-registered ground-to-space image pairs with real atmospheric PSF variation. Experiments demonstrate that FluxFlow consistently outperforms existing baseline methods in both photometric and scientific accuracy.

Shuhong Liu, Xining Ge, Ziteng Cui +8

1The University of Tokyo · 2I2WM · 3Tohoku University +1

Flow Matching Image Super-Resolution

May 5, 2026q-bio.QM

Tree-Conditioned Edit Flows for Ancestral Sequence Reconstruction

Ancestral sequence reconstruction (ASR) aims to infer extinct protein sequences at internal nodes of a phylogenetic tree. Classical ASR methods are typically based on continuous-time Markov substitution models, but they treat sites largely independently and handle insertions and deletions only weakly or not at all. We introduce a tree-conditioned edit-flow model for variable-length ASR. Given two descendant sequences and their branch distances to a shared ancestor, the model reconstructs the ancestor through paired bidirectional edit trajectories constrained to agree on a common ancestral state. On a benchmark of experimentally evolved sequences with only context-independent substitutions, the model does not match the accuracy of the best classical method, yet still achieves reasonable performance despite being trained on natural sequences that include insertions, deletions, and substitutions. On a benchmark of natural homologous sequences with abundant insertions and deletions, the model most accurately localizes inferred evolutionary change.

Emil Sharafutdinov, Ingemar André

Center for Molecular Protein Science Lund University Box 124, 221 00 Lund

Flow Matching Phylogenetic Inference Sequence Modeling Discrete Flow Matching

May 5, 2026cs.LG

Flow Matching on Symmetric Spaces

We introduce a general framework for training flow matching models on Riemannian symmetric spaces, a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate flow matching on symmetric spaces as flow matching on a subspace of the Lie algebra of their isometry group, thus linearizing the problem and greatly simplifying the handling of geodesics. As an application, we showcase our framework on the real Grassmannians

\operatorname{SO}(n) / \operatorname{SO}(k) \times \operatorname{SO}(n-k)

.

Francesco Ruscelli, Ferdinando Zanchetta, Rita Fioresi

Institute for Mathematics University of Heidelberg 69120 Heidelberg, Germany · Department of Pharmacy and Biotechnologies University of Bologna Bologna, Italy

Flow Matching Riemannian Flow Matching Riemannian Geometry

May 4, 2026cs.CV

Mixture Prototype Flow Matching for Open-Set Supervised Anomaly Detection

Open-set supervised anomaly detection (OSAD) aims to identify unseen anomalies using limited anomalous supervision. However, existing prototype-based methods typically model normal data via a unimodal Gaussian prior, failing to capture inherent multi-modality and resulting in blurred decision boundaries. To address this, we propose Mixture Prototype Flow Matching (MPFM), a framework that learns a continuous transformation from normal feature distributions to a structured Gaussian mixture prototype space. Departing from traditional flow-based approaches that rely on a single velocity vector, MPFM explicitly models the velocity field as a Gaussian mixture prior where each component corresponds to a distinct normal class. This design facilitates mode-aware and semantically coherent distribution transport. Furthermore, we introduce a Mutual Information Maximization Regularizer (MIMR) to prevent prototype collapse and maximize normal-anomaly separability. Extensive experiments demonstrate that MPFM achieves state-of-the-art performance across diverse benchmarks under both single- and multi-anomaly settings.

Fuyun Wang, Yuanzhi Wang, Xu Guo +6

Nanjing University of Science and Technology, Nanjing, China · Beijing Normal University, Beijing, China · China Academy of Space Technology, Beijing, China +1

Flow Matching Prototype Learning Anomaly Detection

May 4, 2026cs.CV

DirectEdit: Step-Level Accurate Inversion for Flow-Based Image Editing

With recent advancements in large-scale pre-trained text-to-image (T2I) models, training-free image editing methods have demonstrated remarkable success. Typically, these methods involve adding noise to a clean image via an inversion process, followed by separate denoising steps for the reconstruction and editing paths during the forward process. However, since the reconstruction path is approximated using noisy latents from mismatched timesteps, existing methods inevitably suffer from accumulated drift, which fundamentally limits reconstruction fidelity. To address this challenge, we systematically analyze the inversion process within the flow transformer and propose DirectEdit, a simple yet effective editing method that eliminates the inherent reconstruction error without introducing additional neural function evaluations (NFEs). Unlike most prior works that attempt to rectify the inversion path, DirectEdit focuses on directly aligning the forward paths, enabling precise reconstruction and reliable feature sharing. Furthermore, we introduce a preservation mechanism based on attention feature injection and multi-branch mask-guided noise blending, which effectively balances fidelity and editability. Extensive experiments across diverse scenarios demonstrate that DirectEdit achieves efficient and accurate image editing, delivering superior performance that outperforms state-of-the-art methods. Code and examples are available at https://desongyang.github.io/Directedit.

Desong Yang, Mang Ye

National Engineering Research Center for Multimedia Software, School of Computer Science, Wuhan University, Wuhan, China.

Flow Matching Text-Guided Image Editing Diffusion-Based Image Editing Image Editing

May 4, 2026cs.GR

Generative Modeling with Orbit-Space Particle Flow Matching

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Sinan Wang, Jinjin He, Shenyifan Lu +3

Georgia Institute of Technology, USA

Flow Matching One-Step Generative Modeling Generative Modeling 3D Shape Generation Permutation-Invariant Learning Flow-Based Generative Modeling

May 2, 2026cs.AI

CoFlow: Coordinated Few-Step Flow for Offline Multi-Agent Decision Making

Generative models have emerged as a promising paradigm for offline multi-agent reinforcement learning (MARL), but existing approaches require many iterative sampling steps. Recent few-step acceleration methods either distill a joint teacher into independent students or apply averaged velocity fields independently to each agent. Unfortunately, these few-step approaches hurt inter-agent coordination. We show that the efficiency-coordination trade-off is not inherent: single-pass multi-agent generation can preserve coordination when the velocity field is natively joint-coupled. We propose Coordinated few-step Flow (CoFlow), an architecture that combines Coordinated Velocity Attention (CVA) with Adaptive Coordination Gating. A finite-difference consistency surrogate further replaces memory-prohibitive Jacobian-vector product backpropagation through the averaged velocity field with two stop-gradient forward passes. Across 60 configurations spanning MPE, MA-MuJoCo, and SMAC, CoFlow matches or surpasses Gaussian policies, value-based methods, transformer policies, diffusion models, and prior flow baselines on episodic return. Three independent coordination probes confirm that CoFlow's improvements arise from inter-agent coordination rather than per-agent capacity. A denoising-step sweep shows that single-pass inference suffices on every configuration. CoFlow reaches state-of-the-art coordination quality in 1-3 denoising steps under both centralized and decentralized execution. Project Page: https://guowei-zou.github.io/coflow/

Guowei Zou, Haitao Wang, Beiwen Zhang +2

Sun Yat-sen University

Flow Matching Multi-Agent Coordination Generative Flow Networks Flow-Based Generative Modeling Multi-Agent Reinforcement Learning Offline MARL

May 2, 2026cs.LG

Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events

Events in spatiotemporal systems are ubiquitous, yet modeling their complex distributions remains challenging. Existing point process models often rely on strong structural assumptions and are typically limited to autoregressive, event-by-event prediction. As a result, they struggle to support broader inference tasks such as inverse inference, trajectory reconstruction, and recovery of missing event locations. We introduce Arbitrarily Conditioned Hierarchical Flows (ARCH), a hierarchical flow matching framework for spatiotemporal event modeling. ARCH is expressive enough to capture complex event distributions while enabling tractable and accurate computation of conditional intensities, which quantify instantaneous event risk. Built on a history-encoder-generative-decoder architecture, ARCH introduces a hybrid masking strategy for flexible conditioning on arbitrary observed events. This enables a unified treatment of forecasting, inverse inference, and partial trajectory recovery within a single framework. Experiments on synthetic and real-world datasets show that ARCH consistently outperforms existing baselines across both prediction and conditional inference tasks.

Keyan Chen, Qiwei Yuan, Zhitong Xu +2

Kahlert School of Computing University of Utah · Celonis AI

Temporal Point Processes Flow Matching Spatiotemporal Forecasting Conditional Generative Modeling

May 1, 2026cs.CV

Posterior Augmented Flow Matching

Flow matching (FM) trains a time-dependent vector field that transports samples from a simple prior to a complex data distribution. However, for high-dimensional images, each training sample supervises only a single trajectory and intermediate point, yielding an extremely sparse and high-variance training signal. This under-constrained supervision can cause flow collapse, where the learned dynamics memorize specific source-target pairings, mapping diverse inputs to overly similar outputs, failing to generalize. We introduce Posterior-Augmented Flow Matching (PAFM), a theoretically grounded generalization of FM that replaces single-target supervision with an expectation over an approximate posterior of valid target completions for a given intermediate state and condition. PAFM factorizes this intractable posterior into (i) the likelihood of the intermediate under a hypothesized endpoint and (ii) the prior probability of that endpoint under the condition, and uses an importance sampling scheme to construct a mixture over multiple candidate targets. We prove that PAFM yields an unbiased estimator of the original FM objective while substantially reducing gradient variance during training by aggregating information from many plausible continuation trajectories per intermediate. Finally, we show that PAFM improves over FM by up to 3.4 FID50K across different model scales (SiT-B/2 and SiT-XL/2), different architectures (SiT and MMDiT), and in both class and text conditioned benchmarks (ImageNet and CC12M), with a negligible increase in the compute overhead. Code: https://github.com/gstoica27/PAFM.git.

George Stoica, Sayak Paul, Matthew Wallingford +6

Georgia Tech · University of Washington · Hugging Face +2

Flow Matching Conditional Image Generation Flow-Based Generative Modeling Variance Reduction

May 1, 2026cs.LG

Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching

Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or propagate approximate covariance through many integration steps, trading off training cost, inference cost, or accuracy. We show that none of these trade-offs is necessary. By extending Tweedie's formula from the denoising setting to the flow matching interpolant, we derive an exact, closed-form expression for the posterior covariance at every point along the generative trajectory. The result depends on a single quantity, namely the divergence of the learned velocity field, which can be computed post-hoc on any pre-trained flow matching model, requiring no retraining and no architectural modification. For one-step generators such as MeanFlow, the same formula yields the end-to-end generation uncertainty in a single forward pass, eliminating the multi-step variance propagation required by all prior methods. Experiments on MNIST confirm that the resulting per-pixel uncertainty maps are semantically meaningful, concentrating on digit boundaries where inter-sample variation is highest, and that the scalar uncertainty score tracks actual prediction error, all at roughly

10^4 \times

less total compute than ensembling or Monte Carlo dropout.

Jiarui Xing, Song Wang, Jian Wang

Yale University · Harvard Medical School

Flow Matching Uncertainty Quantification Bayesian Inference Flow-Based Generative Modeling Covariance Estimation Uncertainty Propagation

May 1, 2026cs.CV

Flow matching for Sentinel-2 super-resolution: implementation, application, and implications

Developing robust techniques for super-resolution of satellite imagery involves navigating commonly observed trade-offs between spectral fidelity and perceptual quality. In this work, we introduce a flow matching model for 4x super-resolution of 10-m Sentinel-2 visible and near-infrared bands over the conterminous United States (CONUS) using a dataset of 120,851 10-m Sentinel-2 and 2.5-m resampled NAIP imagery pairs acquired on the same day. Our results showed that the flow matching model outperformed diffusion and Real-ESRGAN models in pixel-wise accuracy in a single sampling step using the Euler method. When evaluated with a second-order Midpoint solver, our model generated perceptually realistic super-resolved imagery in only 20 sampling steps, effectively navigating the perception-distortion trade-off at inference time without retraining. We used this model to produce a super-resolved 2.5-m 4-band CONUS imagery product derived from 2025 10-m Sentinel-2 annual composites, consisting of over 1.58 trillion pixels. We further evaluated the use of super-resolved data on a land cover classification task using semantic segmentation models. Finally, we generated a yearly 2.5-m land cover product for the Chesapeake Bay watershed for 2020-2025. An accuracy assessment against 25,000 ground truth points revealed an overall accuracy of 89.11% for the annual land cover product. We conclude that flow matching is an effective generative modeling approach for super-resolution of Sentinel-2 imagery compared to diffusion and Generative Adversarial Network-based methods, and has strong implications for expanding access to high-resolution imagery for geospatial applications that demand fine spatial detail.

Dakota Hester, Vitor S. Martins, Lucas B. Ferreira +2

Department of Agricultural and Biological Engineering, Mississippi State University · North Mississippi Research and Extension Center, Mississippi State University

Flow Matching Land Cover Classification Remote Sensing Image Super-Resolution Remote Sensing Image Super-Resolution

May 1, 2026cs.LG

Binomial flows: Denoising and flow matching for discrete ordinal data

Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting where common approaches focus on learning discrete scores and rates. In this work we close this gap for discrete non-negative ordinal data by introducing Binomial flows. Our framework provides a simple recipe for training a discrete diffusion model which simultaneously denoises, samples, and estimates exact likelihoods. We verify our methodology on synthetic examples and obtain competitive results on real-world data sets.

Yair Shenfeld, Ricardo Baptista, Stefano Peluchetti

Flow Matching Flow-Based Generative Modeling Diffusion Models Discrete Flow Matching

May 1, 2026cs.LG

Free Energy Surface Sampling via Reduced Flow Matching

Sampling the free energy surface, namely, the distribution of collective variables (CVs), is a crucial problem in statistical physics, as it underpins a better understanding of chemical reactions and conformational transitions. Traditional methods for free energy surface sampling involve simulation in high-dimensional configuration space and projecting the resulting configurations onto the CV space. To reduce the computational costs of such sampling, we propose FES-FM, a reduced flow matching (FM) method for free energy sampling (FES). We train a dynamical transport map in the CV space, thereby enabling direct sampling of the free energy surface. For many-particle systems, we construct a prior distribution based on the Hessian at a local minimum of the potential, which ensures both rotation-translation invariance and physically meaningful configurations. We evaluate the proposed method across a variety of potential functions and collective variables. Comparative experiments demonstrate that our approach drastically reduces computational costs while delivering superior accuracy per unit sampling time.

Zichen Liu, Tiejun Li

Center for Data Science, Peking University · LMAM and School of Mathematical Sciences, Peking University · Center for Machine Learning Research, Peking University

Free Energy Calculation Flow Matching Molecular Dynamics Simulation

Apr 30, 2026cs.LG

StyleShield: Exposing the Fragility of AIGC Detectors through Continuous Controllable Style Transfer

AI-generated content (AIGC) detectors are increasingly deployed in high-stakes settings such as academic integrity screening, yet their reliability rests on a fundamental paradox: as language models are trained on human-written corpora, the statistical boundary between AI and human writing will inevitably dissolve as models improve. Commercial incentives have further distorted this landscape -- detection services and "de-AIification" tools often operate within the same supply chain, replacing evaluation of content quality with judgment of content origin. We present StyleShield, the first flow matching framework for conditional text style transfer, operating directly in continuous token embedding space via a DiT backbone with zero-initialized cross-attention adapters conditioned on frozen Qwen-7B representations. At inference, we adapt the SDEdit paradigm from image synthesis to text embeddings, with a single parameter gamma providing smooth continuous control over the evasion-preservation trade-off. On a multi-domain Chinese benchmark, StyleShield achieves 94.6% evasion against the training detector and >=99% against three unseen detectors, maintaining 0.928 semantic similarity. We further introduce RateAudit, a document-level scheduling algorithm that demonstrates detection-rate verdicts can be set to arbitrary values, directly questioning the reliability of score-based evaluation.

Guantian Zheng

Flow Matching AI-Generated Text Detection Robustness of Machine-Generated Text Detection Text Generation Adversarial Text Attacks

Apr 28, 2026cs.RO

FlowS: One-Step Motion Prediction via Local Transport Conditioning

Generative motion prediction must satisfy three simultaneous requirements for real-world autonomy: high accuracy, diverse multimodal futures, and strictly bounded latency. Diffusion models meet the first two but violate the third, requiring tens to hundreds of denoising steps. We identify a conditioning strategy that resolves this tension: \textit{single-step integration is accurate when the underlying transport problem is local}. A model that must both discover the correct behavioral mode and traverse a long displacement in one step accumulates large discretization errors; conditioning the base distribution to lie near plausible futures reduces the problem to short-range refinement, the regime where a single Euler step suffices. We instantiate this \emph{local transport conditioning} in FlowS, a conditional flow matching framework with two mechanisms. First, an online, scene-conditioned learned prior emits

K

calibrated anchor trajectories per agent, each already near a plausible future, converting mode discovery into local correction. Second, a step-consistent displacement field enforces semigroup self-consistency, guaranteeing that a single step inherits multi-step accuracy. Crucially, anchoring this field at learned priors along straight-line paths yields a {stable, low-variance} training target, unlike prior self-consistency methods that suffer from {high-variance bootstrap} signals on curved diffusion paths. On the Waymo Open Motion Dataset, FlowS achieves state-of-the-art Soft mAP {(0.4804) and mAP (0.4703) with ensemble at 75,FPS} with single-step inference, demonstrating that local transport conditioning makes one-step generative motion prediction practical for safety-critical autonomy. Code and pretrained models will be released upon acceptance.

Leandro Di Bella, Adrian Munteanu, Bruno Cornelis

Department of Electronics and Informatics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium · IMEC, Kapeldreef 75, B-3001 Leuven, Belgium

Flow Matching Trajectory Generation Multi-Agent Trajectory Prediction Autonomous Driving Perception One-Step Generative Modeling Flow-Based Generative Modeling+2

Apr 28, 2026q-bio.QM

PhyloSDF: Phylogenetically-Conditioned Neural Generation of 3D Skull Morphology via Residual Flow Matching

Generating novel, biologically plausible three-dimensional morphological structures is a fundamental challenge in computational evolutionary biology, hampered by extreme data scarcity and the requirement that generated shapes respect phylogenetic relationships among species. In this work, we present PhyloSDF, a phylogenetically-conditioned neural generative model for 3D biological morphology that integrates two innovations: (1) a DeepSDF auto-decoder regularized by a novel Phylogenetic Consistency Loss that structures the latent space to correlate with evolutionary distances (Pearson r=0.993); (2) a Residual Conditional Flow Matching (Residual CFM) architecture that factorizes generation into analytic species-centroid lookup and learned residual prediction, enabling generation from as few as ~4 specimens per species. We evaluate PhyloSDF on 100 micro-CT-scanned skulls of Darwin's Finches and their relatives across 24 species. The model generates novel meshes achieving 88-129% of real intra-species variation at the code level, with all 180 generated meshes verified as non-memorized. Residual CFM surpasses denoising diffusion (which fails entirely at this scale), standard flow matching (which mode-collapses to 3-6% variation), and a Gaussian mixture baseline in both fidelity (Chamfer Distance 0.00181 vs. 0.00190) and morphometric Fréchet distance (10,641 vs. 13,322). Leave-one-species-out experiments across 18 species demonstrate phylogenetic extrapolation capability, and smooth latent interpolations produce biologically plausible ancestral skull reconstructions.

Kaikwan Lau, Gary P. T. Choi

Department of Mathematics The Chinese University of Hong Kong

Flow Matching 3D Mesh Generation 3D Shape Generation Conditional Generative Modeling

Apr 27, 2026q-bio.MN

Learning biophysical models of gene regulation with probability flow matching

Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although single-cell RNA sequencing provides quantitative snapshots of the transcriptome, current methods for inferring gene-regulatory dynamics often lack mechanistic interpretability and fail to generalize to unseen conditions. Here we introduce Probability Flow Matching (PFM), a scalable framework for learning biophysically consistent stochastic processes directly from time-resolved single-cell measurements. Applying PFM to three hematopoiesis datasets, we show that models with similar interpolation accuracy can encode fundamentally different dynamics, with only biophysically consistent formulations accurately capturing mechanisms of lineage transitions, fate specification, and gene perturbation responses. We further demonstrate that PFM accommodates unbalanced populations, enabling simultaneous inference of cellular proliferation and death dynamics. Together, these results establish PFM as a flexible, scalable framework for integrating mechanistic modeling with single-cell omics.

Suryanarayana Maddu, Victor Chardès, Michael J. Shelley

Center for Computational Biology, Flatiron Institute, New York, NY, USA, 10010 · Molecular & Cellular Biology Department, Harvard University, Cambridge, MA 02138 · Courant Institute of Mathematical Sciences, New York University, New York, NY, USA, 10012

Flow Matching Single-Cell Perturbation Modeling Gene Regulatory Network Inference Single-Cell Transcriptomics

Apr 27, 2026cs.CV

Point-MF: One-step Point Cloud Generation from a Single Image via Mean Flows

Single-image point cloud reconstruction must infer complete 3D geometry, including occluded parts, from a single RGB image. While diffusion-based reconstructors achieve high accuracy, they typically require many denoising iterations, resulting in slow and expensive inference. We propose Point-MF, a Mean-Flow-based framework for low-NFE single-image point cloud reconstruction that couples a Mean-Flow-compatible architecture with an auxiliary loss. Specifically, Point-MF operates directly in point-cloud space to learn the mean velocity field and enables one-step reconstruction with a single network function evaluation (1-NFE), without relying on VAE-based latent representations. To make Mean Flow effective under large interval jumps, Point-MF employs a Diffusion Transformer tailored to the Mean-Flow setting, conditioned on frozen DINOv3 image features via a lightweight token adapter and equipped with explicit interval/time conditioning. Moreover, we introduce Denoised Space Anchor, a set-distance auxiliary loss on the denoised-space estimate

x_θ

induced by the predicted velocity field, to stabilize large-step generation and reduce outliers and density artifacts. On ShapeNet-R2N2 and Pix3D, Point-MF strikes a strong balance between reconstruction quality and inference speed compared to multi-step diffusion baselines and competitive feedforward models, while generating high-quality point clouds with millisecond-level latency.

Yuta Baba, Keiji Yanai

The University of Electro-Communications 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan

Flow Matching One-Step Generative Modeling Mean Flow Point Cloud Generation Single-View 3D Reconstruction

Apr 26, 2026cs.AR

FlowPlace: Flow Matching for Chip Placement

Chip placement plays an important role in physical design. While generative models like diffusion models offer promising learning-based solutions, current methods have the following limitations: they use random synthetic data for pre-training, require long sampling times, and often result in overlaps due to their dependence on gradient-based solvers during the sampling process. To overcome these issues, we propose FlowPlace, which features mask-guided synthetic data generation, flow-based efficient training with flexible prior injection, and hard constraint sampling for overlap-free layouts. Experiments on OpenROAD and ICCAD 2015 benchmarks show FlowPlace achieves better PPA metrics, 10-50

\times

faster sampling efficiency, and zero overlaps.

Peng Xie, Ke Xue, Yunqi Shi +6

1State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Artificial Intelligence, Nanjing University, China · 3Huawei Noah’s Ark Lab, China

Constrained Generative Modeling Flow Matching Electronic Design Automation Generative Modeling Flow-Based Generative Modeling

Apr 26, 2026cs.CV

Adversarial Flow Matching for Imperceptible Attacks on End-to-End Autonomous Driving

Autonomous driving (AD) is evolving towards end-to-end (E2E) frameworks through two primary paradigms: monolithic models exemplified by Vision-Language-Action (VLA), and specialized modular architectures. Despite their divergent designs, both paradigms increasingly rely on Transformer backbones for complex reasoning, potentially causing a shared vulnerability: visually imperceptible perturbations can manipulate E2E AD models into hazardous maneuvers by targeting the Transformer module. Most existing adversarial attack approaches against AD systems operate under white-box or black-box settings; yet, they typically necessitate full model transparency, or suffer from either prohibitive query latency or limited attack transferability. In this paper, we propose Adversarial Flow Matching (AFM), a novel gray-box attack framework that exploits Transformer structural vulnerabilities in E2E AD models. AFM enables efficient one-step generation of adversarial examples via a neural average velocity field. Additionally, the proposed technique yields effective and visually imperceptible attacks by synergistically perturbing the generative latent space and the neural average velocity field. Extensive experiments demonstrate that AFM achieves a superior trade-off between attack effectiveness and imperceptibility: it substantially degrades the performance of both VLA and modular AD agents across various scenarios compared to baselines, while maintaining state-of-the-art visual imperceptibility. Furthermore, adversarial examples generated by AFM exhibit robust cross-model transferability, indicating that AFM closely approximates a black-box attack setting while requiring only the prior knowledge that the target AD model incorporates a Transformer-based module.

Xinyu Zeng, Xiangkun He, Lei Tao +2

Shenzhen Institute for Advanced Study, University of Electronic Science and Technology of China, Shenzhen 518110, China · School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798 · School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Flow Matching End-to-End Autonomous Driving Adversarial Attacks Adversarial Transferability