Flow-Based Generative Modeling

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Overview

Flow-based generative modeling represents generation as a transformation of probability mass, often by integrating a continuous-time velocity field from noise to data or composing invertible normalizing-flow layers. Flow matching and rectified flow train velocity fields by regression along selected paths; optimal-transport couplings, stochastic interpolants, discrete Markov flows, and flow maps extend the toolkit to different data types and sampling budgets. Researchers apply these methods to images, language, molecules, physical fields, and robot actions, assessing fidelity and diversity alongside likelihood, constraint satisfaction, calibration, and runtime. A central challenge is achieving one- or few-step generation without sacrificing quality or mode coverage, while improving path design, robustness, geometric and physical consistency, and theoretical guarantees.

Latest papers

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563 papers125 papers in the last four weeks, up 131% on the four weeks before. 0.7% of all new papers.

Mar 16, 2026

Generative Inverse Design with Abstention via Diagonal Flow Matching

Inverse design aims to find design parameters xx achieving target performance y∗y^*. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag--CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields substantially lower round-trip error than CFM and invertible neural network baselines across design dimensions up to P=784P{=}784, including order-of-magnitude gains on several benchmarks. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, scalable analytical benchmarks, a photonics inverse-design task, and an image-statistics benchmark.

Miguel de Campos, Werner Krebs, Hanno Gottschalk

Institute of Mathematics, TU Berlin · Siemens Energy

Flow MatchingUncertainty QuantificationFlow-Based Generative ModelingInverse Design
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Mar 16, 2026

Conditional Rectified Flow-based End-to-End Rapid Seismic Inversion Method

Seismic inversion is a core problem in geophysical exploration, where traditional methods suffer from high computational costs and are susceptible to initial model dependence. In recent years, deep generative model-based seismic inversion methods have achieved remarkable progress, but existing generative models struggle to balance sampling efficiency and inversion accuracy. This paper proposes an end-to-end fast seismic inversion method based on Conditional Rectified Flow[1], which designs a dedicated seismic encoder to extract multi-scale seismic features and adopts a layer-by-layer injection control strategy to achieve fine-grained conditional control. Experimental results demonstrate that the proposed method achieves excellent inversion accuracy on the OpenFWI[2] benchmark dataset. Compared with Diffusion[3,4] methods, it achieves sampling acceleration; compared with InversionNet[5,6,7] methods, it achieves higher accuracy in generation. Our zero-shot generalization experiments on Marmousi[8,9] real data further verify the practical value of the method. Experimental results show that the proposed method achieves excellent inversion accuracy on the OpenFWI benchmark dataset; compared with Diffusion methods, it achieves sampling acceleration while maintaining higher accuracy than InversionNet methods; experiments based on the Marmousi standard model further verify that this method can generate high-quality initial velocity models in a zero-shot manner, effectively alleviating the initial model dependency problem in traditional Full Waveform Inversion (FWI), and possesses industrial practical value.

Haofei Xu, Wei Cheng, Sizhe Li +1

School of Electronic lnformation and Electrical Engineering, Yangtze UniversityJingzhou, Hubei 434023, PR.China

Inverse ProblemsConditional Generative ModelingFlow-Based Generative Modeling
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Mar 16, 2026

Faster Inference of Flow-Based Generative Models via Improved Data-Noise Coupling

Conditional Flow Matching (CFM), a simulation-free method for training continuous normalizing flows, provides an efficient alternative to diffusion models for key tasks like image and video generation. The performance of CFM in solving these tasks depends on the way data is coupled with noise. A recent approach uses minibatch optimal transport (OT) to reassign noise-data pairs in each training step to streamline sampling trajectories and thus accelerate inference. However, its optimization is restricted to individual minibatches, limiting its effectiveness on large datasets. To address this shortcoming, we introduce LOOM-CFM (Looking Out Of Minibatch-CFM), a novel method to extend the scope of minibatch OT by preserving and optimizing these assignments across minibatches over training time. Our approach demonstrates consistent improvements in the sampling speed-quality trade-off across multiple datasets. LOOM-CFM also enhances distillation initialization and supports high-resolution synthesis in latent space training.

Aram Davtyan, Leello Tadesse Dadi, Volkan Cevher +1

University of Bern, Bern, Switzerland · EPFL, Lausanne, Switzerland

Flow-Based Generative ModelingConditional Flow MatchingOptimal Transport
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Mar 16, 2026

TrajFlow: Nation-wide Pseudo GPS Trajectory Generation with Flow Matching Models

The importance of mobile phone GPS trajectory data is widely recognized across many fields, yet the use of real data is often hindered by privacy concerns, limited accessibility, and high acquisition costs. As a result, generating pseudo-GPS trajectory data has become an active area of research. Recent diffusion-based approaches have achieved strong fidelity but remain limited in spatial scale (small urban areas), transportation-mode diversity, and efficiency (requiring numerous sampling steps). To address these challenges, we introduce TrajFlow, which to the best of our knowledge is the first flow-matching-based generative model for GPS trajectory generation. TrajFlow leverages the flow-matching paradigm to improve robustness and efficiency across multiple geospatial scales, and incorporates a trajectory harmonization and reconstruction strategy to jointly address scalability, diversity, and efficiency. Using a nationwide mobile phone GPS dataset with millions of trajectories across Japan, we show that TrajFlow or its variants consistently outperform diffusion-based and deep generative baselines at urban, metropolitan, and nationwide levels. As the first nationwide, multi-scale GPS trajectory generation model, TrajFlow demonstrates strong potential to support inter-region urban planning, traffic management, and disaster response, thereby advancing the resilience and intelligence of future mobility systems.

Peiran Li, Jiawei Wang, Haoran Zhang +4

Hitotsubashi University · The University of Tokyo · LocationMind Inc. +1

Trajectory GenerationFlow-Based Generative Modeling
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Mar 15, 2026

AR-Flow VAE: A Structured Autoregressive Flow Prior Variational Autoencoder for Unsupervised Blind Source Separation

Blind source separation (BSS) seeks to recover latent source signals from observed mixtures. Variational autoencoders (VAEs) offer a natural perspective for this problem: the latent variables can be interpreted as source components, the encoder can be viewed as a demixing mapping from observations to sources, and the decoder can be regarded as a remixing process from inferred sources back to observations. In this work, we propose AR-Flow VAE, a novel VAE-based framework for BSS in which each latent source is endowed with a parameter-adaptive autoregressive flow prior. This prior significantly enhances the flexibility of latent source modeling, enabling the framework to capture complex non-Gaussian behaviors and structured dependencies, such as temporal correlations, that are difficult to represent with conventional priors. In addition, the structured prior design assigns distinct priors to different latent dimensions, thereby encouraging the latent components to separate into different source signals under heterogeneous prior constraints. Experimental results validate the effectiveness of the proposed architecture for blind source separation. More importantly, this work provides a foundation for future investigations into the identifiability and interpretability of AR-Flow VAE.

Yuan-Hao Wei, Fu-Hao Deng, Lin-Yong Cui +1

Hong Kong Polytechnic University · Wuhan University of Technology · The University of Hong Kong

Variational AutoencodersFlow-Based Generative Modeling
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Mar 15, 2026

GoldenStart: Q-Guided Priors and Entropy Control for Distilling Flow Policies

Flow-matching policies hold great promise for reinforcement learning (RL) by capturing complex, multi-modal action distributions. However, their practical application is often hindered by prohibitive inference latency and ineffective online exploration. Although recent works have employed one-step distillation for fast inference, the structure of the initial noise distribution remains an overlooked factor that presents significant untapped potential. This overlooked factor, along with the challenge of controlling policy stochasticity, constitutes two critical areas for advancing distilled flow-matching policies. To overcome these limitations, we propose GoldenStart (GSFlow), a policy distillation method with Q-guided priors and explicit entropy control. Instead of initializing generation from uninformed noise, we introduce a Q-guided prior modeled by a conditional VAE. This state-conditioned prior repositions the starting points of the one-step generation process into high-Q regions, effectively providing a "golden start" that shortcuts the policy to promising actions. Furthermore, for effective online exploration, we enable our distilled actor to output a stochastic distribution instead of a deterministic point. This is governed by entropy regularization, allowing the policy to shift from pure exploitation to principled exploration. Our integrated framework demonstrates that by designing the generative startpoint and explicitly controlling policy entropy, it is possible to achieve efficient and exploratory policies, bridging the generative models and the practical actor-critic methods. We conduct extensive experiments on offline and online continuous control benchmarks, where our method significantly outperforms prior state-of-the-art approaches. Code will be available at https://github.com/ZhHe11/GSFlow-RL.

He Zhang, Ying Sun, Hui Xiong

Thrust of Artificial Intelligence, The Hong Kong University of Science and Technology (Guangzhou) · AI2 Robotics · Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong SAR

Policy DistillationContinuous ControlFlow-Based Generative ModelingRL for Generative Models
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Mar 14, 2026

Discriminative Flow Matching Via Local Generative Predictors

Traditional discriminative computer vision relies predominantly on static projections, mapping input features to outputs in a single computational step. Although efficient, this paradigm lacks the iterative refinement and robustness inherent in biological vision and modern generative modelling. In this paper, we propose Discriminative Flow Matching, a framework that reformulates classification and object detection as a conditional transport process. By learning a vector field that continuously transports samples from a simple noise distribution toward a task-aligned target manifold -- such as class embeddings or bounding box coordinates -- we are at the interface between generative and discriminative learning. Our method attaches multiple independent flow predictors to a shared backbone. These predictors are trained using local flow matching objectives, where gradients are computed independently for each block. We formulate this approach for standard image classification and extend it to the complex task of object detection, where targets are high-dimensional and spatially distributed. This architecture provides the flexibility to update blocks either sequentially to minimise activation memory or in parallel to suit different hardware constraints. By aggregating the predictions from these independent flow predictors, our framework enables robust, generative-inspired inference across diverse architectures, including CNNs and vision transformers.

Om Govind Jha, Manoj Bamniya, Ayon Borthakur

Indian Institute of Science Education and Research Bhopal, India · Indian Institute of Technology Guwahati, India

Flow MatchingObject DetectionImage ClassificationFlow-Based Generative Modeling
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Mar 14, 2026

KoopmanFlow: Spectrally Decoupled Generative Control Policy via Koopman Structural Bias

Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial features, their underlying Probability Flow ODEs apply a uniform temporal integration schedule. Compressed to a single step for real-time Receding Horizon Control (RHC), uniform ODE solvers mathematically smooth over sparse, high-frequency transients entangled within low-frequency steady states. To decouple these dynamics without accumulating pipelined errors, we introduce KoopmanFlow, a parameter-efficient generative policy guided by a Koopman-inspired structural inductive bias. Operating in a unified multimodal latent space with visual context, KoopmanFlow bifurcates generation at the terminal stage. Because visual conditioning occurs before spectral decomposition, both branches are visually guided yet temporally specialized. A macroscopic branch anchors slow-varying trajectories via single-step Consistency Training, while a transient branch uses Flow Matching to isolate high-frequency residuals stimulated by sudden visual cues (e.g., contacts or occlusions). Guided by an explicit spectral prior and optimized via a novel asymmetric consistency objective, KoopmanFlow establishes a fused co-training mechanism. This allows the variant branch to absorb localized dynamics without multi-stage error accumulation. Extensive experiments show KoopmanFlow significantly outperforms state-of-the-art baselines in contact-rich tasks requiring agile disturbance rejection. By trading a surplus latency buffer for a richer structural prior, KoopmanFlow achieves superior control fidelity and parameter efficiency within real-time deployment limits.

Chengsi Yao, Ge Wang, Kai Kang +9

ISing AI · Future Network of Intelligence Institution, The Chinese University of Hong Kong, Shenzhen · Guangdong Polytechnic Normal University +1

Robotic ManipulationFlow-Based Generative ModelingVision-Based Robot Control
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Mar 13, 2026

3DTCR: Vortex-following generative reconstruction improves tropical cyclone intensity prediction from global AI weather forecasts

Global numerical weather prediction (NWP) and artificial intelligence (AI) models often underestimate tropical cyclone (TC) intensity, partly because coarse grids underresolve fine-scale three-dimensional inner-core structures that influence TC intensity evolution. Kilometer-scale NWP simulations can better resolve these structures but are too costly for operational use, which also makes high-resolution TC data limited. Here we construct a 3-km, TC-centered dataset for 2018--2024 using the Weather Research and Forecasting (WRF) model and develop 3DTCR, a vortex-following generative framework that reconstructs three-dimensional TC structure from FuXi global forecasts. 3DTCR combines conditional flow matching (CFM) with two-stage training to learn a coarse-to-fine mapping from center-aligned reanalysis simulation pairs and then adapt it to forecast inputs through latent space alignment. Evaluated on 2024 western North Pacific (WNP) forecasts, 3DTCR reduces the root mean square error (RMSE) and the magnitude of the mean bias error (MBE) in maximum 10-m wind speed by 36.5% and 60.7% relative to FuXi, and by 8.9% and 28.2% relative to the European Centre for Medium-Range Weather Forecasts high-resolution system (ECMWF-HRES), respectively. Case studies suggest that reconstructions capture wind gradients between the eye and eyewall, vertical structure of horizontal winds, and vortex asymmetries, while inheriting the FuXi-predicted TC tracks. 3DTCR generates 5-day TC-centered atmospheric fields in approximately 3 minutes on one GPU, whereas a full-basin 3-km WRF simulation takes about 400 hours on 32 CPU cores. These results demonstrate that such a vortex-following generative reconstruction can add localized three-dimensional detail to global forecasts and improve TC intensity prediction without basin-wide kilometer-scale numerical integration.

Jun Liu, Xiaohui Zhong, Kai Zheng +5

Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, 200433, China. · Department of Atmospheric and Oceanic Sciences, Institute of Atmospheric Sciences, Fudan University, Shanghai, 200438, China. · Shanghai Academy of Artificial Intelligence for Science, Shanghai, 200232, China.

Tropical Cyclone Intensity ForecastingWeather Forecasting3D ReconstructionPhysics-Informed Generative ModelingFlow-Based Generative Modeling
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Mar 13, 2026

Improving Channel Estimation via Multimodal Diffusion Models with Flow Matching

Deep generative models offer a powerful alternative to conventional channel estimation by learning complex channel distributions. By integrating the rich environmental information available in modern sensing-aided networks, this paper proposes MultiCE-Flow, a multimodal channel estimation framework based on flow matching and diffusion transformer (DiT). We design a specialized multimodal perception module that fuses LiDAR, camera, and location data into a semantic condition, while treating sparse pilots as a structural condition. These conditions guide a DiT backbone to reconstruct high-fidelity channels. Unlike standard diffusion models, we employ flow matching to learn a linear trajectory from noise to data, enabling efficient one-step sampling. By leveraging environmental semantics, our method mitigates the ill-posed nature of estimation with sparse pilots. Extensive experiments demonstrate that MultiCE-Flow consistently outperforms traditional baselines and existing generative models. Notably, it exhibits superior robustness to out-of-distribution scenarios and varying pilot densities, making it suitable for environment-aware communication systems.

Xiaotian Fan, Xingyu Zhou, Le Liang +2

School of Information Science and Engineering, Southeast University, Nanjing 210096, China · Purple Mountain Laboratories, Nanjing 211111, China

Channel EstimationMultimodal Diffusion ModelsFlow-Based Generative Modeling
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Mar 13, 2026

VGGT-World: Transforming VGGT into an Autoregressive Geometry World Model

World models that forecast scene evolution by generating future video frames devote the bulk of their capacity to photometric details, yet the resulting predictions often remain geometrically inconsistent. We present VGGT-World, a geometry world model that side-steps video generation entirely and instead forecasts the temporal evolution of frozen geometry-foundation-model (GFM) features. Concretely, we repurpose the latent tokens of a frozen VGGT as the world state and train a lightweight temporal flow transformer to autoregressively predict their future trajectory. Two technical challenges arise in this high-dimensional (d=1024) feature space: (i) standard velocity-prediction flow matching collapses, and (ii) autoregressive rollout suffers from compounding exposure bias. We address the first with a clean-target (z-prediction) parameterization that yields a substantially higher signal-to-noise ratio, and the second with a two-stage latent flow-forcing curriculum that progressively conditions the model on its own partially denoised rollouts. Experiments on KITTI, Cityscapes, and TartanAir demonstrate that VGGT-World significantly outperforms the strongest baselines in depth forecasting while running 3.6-5 times faster with only 0.43B trainable parameters, establishing frozen GFM features as an effective and efficient predictive state for 3D world modeling.

Xiangyu Sun, Shijie Wang, Fengyi Zhang +5

UQMM Lab, The University of Queensland · Beijing Jiaotong University

3D Scene PredictionWorld Model LearningFlow-Based Generative ModelingDense Prediction
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Mar 13, 2026

From Sparse to Dense: Multi-View GRPO for Flow Models via Augmented Condition Space

Group Relative Policy Optimization (GRPO) has emerged as a powerful framework for preference alignment in text-to-image (T2I) flow models. However, we observe that the standard paradigm where evaluating a group of generated samples against a single condition suffers from insufficient exploration of inter-sample relationships, constraining both alignment efficacy and performance ceilings. To address this sparse single-view evaluation scheme, we propose Multi-View GRPO (MV-GRPO), a novel approach that enhances relationship exploration by augmenting the condition space to create a dense multi-view reward mapping. Specifically, for a group of samples generated from one prompt, MV-GRPO leverages a flexible Condition Enhancer to generate semantically adjacent yet diverse captions. These captions enable multi-view advantage re-estimation, capturing diverse semantic attributes and providing richer optimization signals. By deriving the probability distribution of the original samples conditioned on these new captions, we can incorporate them into the training process without costly sample regeneration. Extensive experiments demonstrate that MV-GRPO achieves superior alignment performance over state-of-the-art methods.

Jiazi Bu, Pengyang Ling, Yujie Zhou +8

Shanghai Jiao Tong University · S-Lab, Nanyang Technological University · Shanghai AI Laboratory +7

RL for Image GenerationGroup Relative Policy OptimizationDiffusion Model AlignmentFlow-Based Generative Modeling
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Mar 12, 2026

Curriculum Sampling: A Two-Phase Curriculum for Efficient Training of Flow Matching

Timestep sampling p(t)p(t) is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from 3.853.85 (Uniform) to 3.223.22 while reaching peak performance at 100100k rather than 150150k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Pengwei Sun

Stanford University

Flow MatchingFlow-Based Generative ModelingCurriculum Learning
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Mar 12, 2026

One-Step Flow Policy: Self-Distillation for Fast Visuomotor Policies

Generative flow and diffusion models provide the continuous, multimodal action distributions needed for high-precision robotic policies. However, their reliance on iterative sampling introduces severe inference latency, degrading control frequency and harming performance in time-sensitive manipulation. To address this problem, we propose the One-Step Flow Policy (OFP), a from-scratch self-distillation framework for high-fidelity, single-step action generation without a pre-trained teacher. OFP unifies a self-consistency loss to enforce coherent transport across time intervals, and a self-guided regularization to sharpen predictions toward high-density expert modes. In addition, a warm-start mechanism leverages temporal action correlations to minimize the generative transport distance. Evaluations across 56 diverse simulated manipulation tasks demonstrate that a one-step OFP achieves state-of-the-art results, outperforming 100-step diffusion and flow policies while accelerating action generation by over 100×100\times. We further integrate OFP into the π0.5π_{0.5} model on RoboTwin 2.0, where one-step OFP surpasses the original 10-step policy. These results establish OFP as a practical, scalable solution for highly accurate and low-latency robot control.

Shaolong Li, Lichao Sun, Yongchao Chen

CSE Department, University of Michigan · Lehigh University · College of AI, Tsinghua University

Visuomotor Policy LearningOne-Step Generative ModelingFlow-Based Generative ModelingRobotic ManipulationSelf-Distillation
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Mar 12, 2026

Generalization and Memorization in Rectified Flow

Generative models based on the Flow Matching objective, particularly Rectified Flow, have emerged as a dominant paradigm for efficient, high-fidelity image synthesis. However, while existing research heavily prioritizes generation quality and architectural scaling, the underlying dynamics of how RF models memorize training data remain largely underexplored. In this paper, we systematically investigate the memorization behaviors of RF through the test statistics of Membership Inference Attacks (MIA). We progressively formulate three test statistics, culminating in a complexity-calibrated metric that successfully decouples intrinsic image spatial complexity from genuine memorization signals. This calibration yields a significant performance surge -- boosting attack AUC by up to 15% and the privacy-critical TPR@1%FPR metric by up to 45% -- establishing the first non-trivial MIA specifically tailored for RF. Leveraging these refined metrics, we uncover a distinct temporal pattern: under standard uniform temporal training, a model's susceptibility to MIA strictly peaks at the integration midpoint, a phenomenon we justify via the network's forced deviation from linear approximations. Finally, we demonstrate that substituting uniform timestep sampling with a Symmetric Exponential (U-shaped) distribution effectively minimizes exposure to vulnerable intermediate timesteps. Extensive evaluations across three datasets confirm that this temporal regularization suppresses memorization while preserving generative fidelity.

Mingxing Rao, Daniel Moyer

Vanderbilt University, Nashville TN 37235, USA

Rectified FlowMembership Inference AttacksMemorization in Generative ModelsGenerative ModelingFlow-Based Generative Modeling
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Mar 12, 2026

Sinkhorn-Drifting Generative Models

We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an attractive term toward the target distribution and a repulsive/self-correction term toward the current model, both expressed via one-sided normalized Gibbs kernels. We show that Sinkhorn divergence yields an analogous cross-minus-self structure, but with each term defined by entropic optimal-transport couplings obtained through two-sided Sinkhorn scaling (i.e., enforcing both marginals). This provides a precise sense in which drifting acts as a surrogate for a Sinkhorn-divergence gradient flow, interpolating between one-sided normalization and full two-sided Sinkhorn scaling. Crucially, this connection resolves an identifiability gap in prior drifting formulations: leveraging the definiteness of the Sinkhorn divergence, we show that zero drift (equilibrium of the dynamics) implies that the model and target measures match. Experiments show that Sinkhorn drifting reduces sensitivity to kernel temperature and improves one-step generative quality, trading off additional training time for a more stable optimization, without altering the inference procedure used by drift methods. These theoretical gains translate to strong low-temperature improvements in practice: on FFHQ-ALAE at the lowest temperature setting we evaluate, Sinkhorn drifting reduces mean FID from 187.7 to 37.1 and mean latent EMD from 453.3 to 144.4, while on MNIST it preserves full class coverage across the temperature sweep. Project page: https://mint-vu.github.io/SinkhornDrifting/

Ping He, Om Khangaonkar, Hamed Pirsiavash +2

Department of Computer Science, Vanderbilt University · Department of Computer Science, University of California, Davis · Department of Computer Science, Purdue University

Sinkhorn DivergenceDrifting ModelsFlow-Based Generative ModelingOptimal TransportOne-Step Generative Modeling
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Mar 12, 2026

EvoFlows: Evolutionary Edit-Based Flow-Matching for Protein Engineering

We introduce EvoFlows, a variable-length protein sequence-to-sequence modeling approach designed for protein engineering. Existing protein language models are poorly suited for optimization tasks: autoregressive models require full sequence generation, masked language and discrete diffusion models rely on pre-specified mutation locations, and no existing methods naturally support insertions and deletions relative to a template sequence. EvoFlows learns mutational trajectories between evolutionarily related protein sequences via edit flows, allowing it to perform a controllable number of mutations (insertions, deletions, and substitutions) on a template sequence, predicting not only which mutation to perform, but also where it should occur. Through extensive in silico evaluation on diverse protein families from UniRef and OAS, we show that EvoFlows generates variants that remain consistent with natural protein families while exploring farther from template sequences than leading baselines.

Nicolas Deutschmann, Constance Ferragu, Jonathan D. Ziegler +2

Cradle

Protein DesignSequence ModelingFlow-Based Generative ModelingFlow Matching
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Mar 11, 2026

COT-FM: Cluster-wise Optimal Transport Flow Matching

We introduce COT-FM, a general framework that reshapes the probability path in Flow Matching (FM) to achieve faster and more reliable generation. FM models often produce curved trajectories due to random or batchwise couplings, which increase discretization error and reduce sample quality. COT-FM fixes this by clustering target samples and assigning each cluster a dedicated source distribution obtained by reversing pretrained FM models. This divide-and-conquer strategy yields more accurate local transport and significantly straighter vector fields, all without changing the model architecture. As a plug-and-play approach, COT-FM consistently accelerates sampling and improves generation quality across 2D datasets, image generation benchmarks, and robotic manipulation tasks.

Chiensheng Chiang, Kuan-Hsun Tu, Jia-Wei Liao +2

National Taiwan University

Flow MatchingGenerative ModelingFlow-Based Generative ModelingImage GenerationOptimal Transport
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Mar 11, 2026

Riemannian MeanFlow for One-Step Generation on Manifolds

Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE. We propose Riemannian MeanFlow (RMF), extending MeanFlow to manifold-valued generation where velocities lie in location-dependent tangent spaces. RMF defines an average-velocity field via parallel transport and derives a Riemannian MeanFlow identity that links average and instantaneous velocities for intrinsic supervision. We make this identity practical in a log-map tangent representation, avoiding trajectory simulation and heavy geometric computations. For stable optimization, we decompose the RMF objective into two terms and apply conflict-aware multi-task learning to mitigate gradient interference. RMF also supports conditional generation via classifier-free guidance. Experiments on spheres, tori, SO(3), and SE(3) demonstrate competitive one-step sampling with improved quality-efficiency trade-offs and substantially reduced sampling cost.

Zichen Zhong, Haoliang Sun, Yukun Zhao +2

School of Software, Shandong University, Jinan, China

Generative ModelingFlow-Based Generative ModelingOne-Step Generative ModelingRiemannian Flow MatchingMean Flow
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Mar 11, 2026

UHD Image Deblurring via Autoregressive Flow with Ill-conditioned Constraints

Ultra-high-definition (UHD) image deblurring poses significant challenges for UHD restoration methods, which must balance fine-grained detail recovery and practical inference efficiency. Although prominent discriminative and generative methods have achieved remarkable results, a trade-off persists between computational cost and the ability to generate fine-grained detail for UHD image deblurring tasks. To further alleviate these issues, we propose a novel autoregressive flow method for UHD image deblurring with an ill-conditioned constraint. Our core idea is to decompose UHD restoration into a progressive, coarse-to-fine process: at each scale, the sharp estimate is formed by upsampling the previous-scale result and adding a current-scale residual, enabling stable, stage-wise refinement from low to high resolution. We further introduce Flow Matching to model residual generation as a conditional vector field and perform few-step ODE sampling with efficient Euler/Heun solvers, enriching details while keeping inference affordable. Since multi-step generation at UHD can be numerically unstable, we propose an ill-conditioning suppression scheme by imposing condition-number regularization on a feature-induced attention matrix, improving convergence and cross-scale consistency. Our method demonstrates promising performance on blurred images at 4K (3840×\times2160) or higher resolutions.

Yucheng Xin, Dawei Zhao, Xiang Chen +6

Shandong Normal University · Qilu University of Technology · Nanjing University of Science and Technology +2

Image DeblurringFlow-Based Generative Modeling
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Mar 11, 2026

Graph-GRPO: Training Graph Flow Models with Reinforcement Learning

Graph generation is a fundamental task with broad applications, such as drug discovery. Recently, discrete flow matching-based graph generation, \aka, graph flow model (GFM), has emerged due to its superior performance and flexible sampling. However, effectively aligning GFMs with complex human preferences or task-specific objectives remains a significant challenge. In this paper, we propose Graph-GRPO, an online reinforcement learning (RL) framework for training GFMs under verifiable rewards. Our method makes two key contributions: (1) We derive an analytical expression for the transition probability of GFMs, replacing the Monte Carlo sampling and enabling fully differentiable rollouts for RL training; (2) We propose a refinement strategy that randomly perturbs specific nodes and edges in a graph, and regenerates them, allowing for localized exploration and self-improvement of generation quality. Extensive experiments on both synthetic and real datasets demonstrate the effectiveness of Graph-GRPO. With only 50 denoising steps, our method achieves 95.0% and 97.5% Valid-Unique-Novelty scores on the planar and tree datasets, respectively. Moreover, Graph-GRPO achieves state-of-the-art performance on the molecular optimization tasks, outperforming graph-based and fragment-based RL methods as well as classic genetic algorithms.

Baoheng Zhu, Deyu Bo, Delvin Ce Zhang +1

Beijing University of Posts and Telecommunications · National University of Singapore · University of Sheffield +1

Graph GenerationFlow-Based Generative ModelingRL for Generative ModelsMolecular Graph Generation
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Mar 10, 2026

From Flow to One Step: Real-Time Multi-Modal Trajectory Policies via Implicit Maximum Likelihood Estimation-based Distribution Distillation

Generative policies based on diffusion and flow matching achieve strong performance in robotic manipulation by modeling multi-modal human demonstrations. However, their reliance on iterative Ordinary Differential Equation (ODE) integration introduces substantial latency, limiting high-frequency closed-loop control. Recent single-step acceleration methods alleviate this overhead but often exhibit distributional collapse, producing averaged trajectories that fail to execute coherent manipulation strategies. We propose a framework that distills a Conditional Flow Matching (CFM) expert into a fast single-step student via Implicit Maximum Likelihood Estimation (IMLE). A bi-directional Chamfer distance provides a set-level objective that promotes both mode coverage and fidelity, enabling preservation of the teacher multi-modal action distribution in a single forward pass. A unified perception encoder further integrates multi-view RGB, depth, point clouds, and proprioception into a geometry-aware representation. The resulting high-frequency control supports real-time receding-horizon re-planning and improved robustness under dynamic disturbances.

Ju Dong, Liding Zhang, Lei Zhang +7

TAMS (Technical Aspects of Multimodal Systems), Department of Informatics, University of Hamburg, Hamburg, Germany. · Technical University of Munich, Germany. · Agile Robots SE, Munich, Germany.

Maximum Marginal Likelihood EstimationRobot Imitation LearningPolicy DistillationEfficient Multimodal InferenceFlow-Based Generative Modeling
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Mar 9, 2026

The Coupling Within: Flow Matching via Distilled Normalizing Flows

Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of coupling measure for sampling noise/data pairs that define the flow matching (FM) regression loss. While FM training defaults usually to independent coupling, recent works show that adaptive couplings informed by noise/data distributions (e.g., via optimal transport, OT) improve both model training and inference. We radicalize this insight by shifting the paradigm: rather than computing adaptive couplings directly, we use distilled couplings from a different, pretrained model capable of placing noise and data spaces in bijection -- a property intrinsic to normalizing flows (NF) through their maximum likelihood and invertibility requirements. Leveraging recent advances in NF image generation via auto-regressive (AR) blocks, we propose Normalized Flow Matching (NFM), a new method that distills the quasi-deterministic coupling of pretrained NF models to train student flow models. These students achieve the best of both worlds: significantly outperforming flow models trained with independent or even OT couplings, while also improving on the teacher AR-NF model.

David Berthelot, Tianrong Chen, Jiatao Gu +6

Flow-Based Generative ModelingFlow MatchingNormalizing Flows
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Mar 9, 2026

Statistical Inference via Generative Models: Flow Matching and Causal Inference

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book reinterprets generative AI in the language of statistics, using flow matching as a central example. The key idea is that generative models should be understood not merely as devices for producing plausible data, but as methods for the nonparametric learning of high-dimensional probability distributions. From this viewpoint, missing-data imputation becomes principled sampling from learned conditional distributions, counterfactual analysis becomes the estimation of intervention distributions, and distributional dynamics become statistically analyzable objects. Mathematically, flow matching represents distributional deformation through the continuity equation and a time-dependent velocity field, thereby extending score matching from the learning of static score fields to the learning of transport paths themselves. Building on this foundation, the book develops a statistical framework in which generative models are used to estimate nuisance components while inferential validity is maintained through orthogonalization and cross-fitting in the spirit of double/debiased machine learning. Applications to survival analysis, censoring, missingness, and causal inference show how generative models can be integrated into statistical inference for structured high-dimensional problems.

Shinto Eguchi

Causal InferenceFlow MatchingFlow-Based Generative Modeling
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Mar 9, 2026

Foley-Flow: Coordinated Video-to-Audio Generation with Masked Audio-Visual Alignment and Dynamic Conditional Flows

Coordinated audio generation based on video inputs typically requires a strict audio-visual (AV) alignment, where both semantics and rhythmics of the generated audio segments shall correspond to those in the video frames. Previous studies leverage a two-stage design where the AV encoders are firstly aligned via contrastive learning, then the encoded video representations guide the audio generation process. We observe that both contrastive learning and global video guidance are effective in aligning overall AV semantics while limiting temporally rhythmic synchronization. In this work, we propose FoleyFlow to first align unimodal AV encoders via masked modeling training, where the masked audio segments are recovered under the guidance of the corresponding video segments. After training, the AV encoders which are separately pretrained using only unimodal data are aligned with semantic and rhythmic consistency. Then, we develop a dynamic conditional flow for the final audio generation. Built upon the efficient velocity flow generation framework, our dynamic conditional flow utilizes temporally varying video features as the dynamic condition to guide corresponding audio segment generations. To this end, we extract coherent semantic and rhythmic representations during masked AV alignment, and use this representation of video segments to guide audio generation temporally. Our audio results are evaluated on the standard benchmarks and largely surpass existing results under several metrics. The superior performance indicates that FoleyFlow is effective in generating coordinated audios that are both semantically and rhythmically coherent to various video sequences.

Shentong Mo, Yibing Song

CMU / MBZUAI · DAMO Academy, Alibaba Group · Hupan Laboratory

Audio-Video GenerationAudio-Visual SynchronizationAudio-Visual AlignmentFlow-Based Generative Modeling
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Mar 6, 2026

Self-Supervised Flow Matching for Scalable Multi-Modal Synthesis

Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit unexpected scaling behavior. We argue that this dependence arises from the model's training objective, which poses a denoising task with little incentive to learn semantic representations. We introduce Self-Flow: a self-supervised flow matching paradigm that integrates representation learning within the generative framework. Our key mechanism, Dual-Timestep Scheduling, applies heterogeneous noise levels across tokens, creating an information asymmetry that forces the model to infer missing information from corrupted inputs. This drives learning strong representations alongside generative capabilities without external supervision. Our method generalizes across modalities and enables multi-modal training while following expected scaling laws, achieving superior image, video, and audio generation.

Hila Chefer, Patrick Esser, Dominik Lorenz +5

Black Forest Labs · MIT

Flow-Based Generative ModelingFlow MatchingMultimodal GenerationSelf-Supervised Learning
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Mar 6, 2026

Training Flow Matching: The Role of Weighting and Parameterization

We study the training objectives of denoising-based generative models, with a particular focus on loss weighting and output parameterization, including noise-, clean image-, and velocity-based formulations. Through a systematic numerical study, we analyze how these training choices interact with the intrinsic dimensionality of the data manifold, model architecture, and dataset size. Our experiments span synthetic datasets with controlled geometry as well as image data, and compare training objectives using quantitative metrics for denoising accuracy (PSNR across noise levels) and generative quality (FID). Rather than proposing a new method, our goal is to disentangle the various factors that matter when training a flow matching model, in order to provide practical insights on design choices.

Anne Gagneux, Ségolène Martin, Rémi Gribonval +1

ENS de Lyon, CNRS, Universit´e Claude Bernard Lyon 1, Inria, LIP, UMR 5668, France · Technische Universität Berlin, Germany · Inria, ENS de Lyon, CNRS, Universit´e Claude Bernard Lyon 1, LIP, UMR 5668, France

Flow MatchingAdaptive Loss WeightingFlow-Based Generative ModelingDiffusion Models
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Mar 6, 2026

LATO: 3D Mesh Flow Matching with Structured TOpology Preserving LAtents

In this paper, we introduce LATO, a novel topology-preserving latent representation that enables scalable, flow matching-based synthesis of explicit 3D meshes. LATO represents a mesh as a Vertex Displacement Field (VDF) anchored on surface, incorporating a sparse voxel Variational Autoencoder (VAE) to compress this explicit signal into a structured, topology-aware voxel latent. To decapsulate the mesh, the VAE decoder progressively subdivides and prunes latent voxels to instantiate precise vertex locations. In the end, a dedicated connection head queries the voxel latent to predict edge connectivity between vertex pairs directly, allowing mesh topology to be recovered without isosurface extraction or heuristic meshing. For generative modeling, LATO adopts a two-stage flow matching process, first synthesizing the structure voxels and subsequently refining the voxel-wise topology features. Compared to prior isosurface/triangle-based diffusion models and autoregressive generation approaches, LATO generates meshes with complex geometry, well-formed topology while being highly efficient in inference.

Tianhao Zhao, Youjia Zhang, Hang Long +7

Huazhong University of Science and Technology · Peking University · Independent Researcher +1

3D Mesh Generation3D Representation LearningFlow-Based Generative Modeling
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Mar 6, 2026

Reflective Flow Sampling Enhancement

The growing demand for text-to-image generation has led to rapid advances in generative modeling. Recently, text-to-image diffusion models trained with flow matching algorithms, such as FLUX, have achieved remarkable progress and emerged as strong alternatives to conventional diffusion models. At the same time, inference-time enhancement strategies have been shown to improve the generation quality and text-prompt alignment of text-to-image diffusion models. However, these techniques are mainly applicable to conventional diffusion models and usually fail to perform well on flow models. To bridge this gap, we propose Reflective Flow Sampling (RF-Sampling), a theoretically-grounded and training-free inference enhancement framework explicitly designed for flow models, especially for the CFG-distilled variants (i.e., models distilled from CFG guidance techniques), like FLUX. Departing from heuristic interpretations, we provide a formal derivation proving that RF-Sampling implicitly performs gradient ascent on the text-image alignment score. By leveraging a linear combination of textual representations and integrating them with flow inversion, RF-Sampling allows the model to explore noise spaces that are more consistent with the input prompt. Extensive experiments across multiple benchmarks demonstrate that RF-Sampling consistently improves both generation quality and prompt alignment. Moreover, RF-Sampling is also the first inference enhancement method that can exhibit test-time scaling ability to some extent on FLUX.

Zikai Zhou, Muyao Wang, Shitong Shao +4

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China. · The University of Tokyo, Japan. · Microsoft, Beijing. +1

T2I Diffusion ModelsFlow-Based Generative ModelingDiffusion Model GuidanceText-Image AlignmentFlow Matching
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Mar 6, 2026

Offline Materials Optimization with CliqueFlowmer

Recent advances in deep learning inspired neural network-based approaches to computational materials discovery (CMD). A plethora of problems in this field involve finding materials that optimize a target property. Nevertheless, the increasingly popular generative modeling methods are ineffective at boldly exploring attractive regions of the materials space due to their maximum likelihood training. In this work, we offer an alternative CMD technique based on offline model-based optimization (MBO) that fuses direct optimization of a target material property into generation. To that end, we introduce a domain-specific model, dubbed CliqueFlowmer, that incorporates recent advances of clique-based MBO into transformer and flow generation. We validate this model's optimization abilities and show that materials it produces strongly outperform those from generative baselines. To support specialized materials discovery applications and broader interdisciplinary research, we release our code, model weights, and additional project resources at https://github.com/znowu/CliqueFlowmer, https://colab.research.google.com/drive/1usUg7zezFkcYHlm2MdYwZUNJXf_YkWnY?usp=sharing, and https://x.com/kuba_AI/status/2033382617442345321.

Jakub Grudzien Kuba, Benjamin Kurt Miller, Sergey Levine +1

BAIR, UC Berkeley, Berkeley, California, USA · FAIR, Meta, San Francisco, California, USA

Materials DiscoveryComputational Materials ScienceFlow-Based Generative Modeling
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