Flow-Based Generative Modeling

Follow this topic Ask about this topic

Momentum

66 papers in the last four weeks, up 288% on the four weeks before. 0.7% of all new papers.

Jul 13Week of Sep 28

Latest papers 331

Jun 10, 2026cs.LG

Flow Matching with In-Context Priors for Out-of-Distribution Brain Dynamics

Flow matching and diffusion models enable conditional generation across domains ranging from images to proteins, with recent extensions to out-of-distribution contexts. Yet generative models of neural time series have largely remained restricted to categorical conditioning, precluding compositional and zero-shot generalization. In this work, we propose a per-timestep conditioned diffusion transformer for generating realistic fMRI brain dynamics during unseen cognitive tasks by injecting both compositional language and optional spatial priors in-context. Such zero-shot generation could enable counterfactual neuroscience by supporting in-silico design and evaluation of novel cognitive experiments before empirical validation. Leveraging this model, we evaluate across hundreds of held-out task conditions and characterize predictive performance in relation to the training manifold. From language alone, the model recovers region-specific recruitment across tasks and held-out spatial activation patterns. Spatial priors, when available, complement the text pathway by anchoring generation in regions of task space where language alone degrades, while retaining the compositional structure needed for counterfactual task specification. To our knowledge this is the first generative model of whole-cortex fMRI dynamics for unseen cognitive tasks, advancing counterfactual neuroscience and data-driven experimental design.

Sam Gijsen, Michał Łukomski, Marc-André Schulz +1

Hertie Institute for AI in Brain Health, University of Tübingen, Germany · Tübingen AI Center, University of Tübingen, Germany · Charité – Universitätsmedizin Berlin, Department of Psychiatry and Psychotherapy, Germany +1

Diffusion Transformer Time Series Generation Flow-Based Generative Modeling Conditional Diffusion Models

Jun 10, 2026cs.LG

Spectrally Regularized Latent Flow Matching for Turbulence Generation

Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a 256^2 DNS dataset at Re_f \approx 2250, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25% to 94% in reconstruction and from 20% to 79% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias -0.70 that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias -0.117 at just 20 function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of S_3, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of S_3 suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.

Khalid Rafiq, Aditya G. Nair

Department of Mechanical Engineering University of Nevada, Reno, NV, USA

Spectral Regularization Flow Matching Flow-Based Generative Modeling Computational Fluid Dynamics

Jun 9, 2026cs.CV

Mean Flow Distillation: Robust and Stable Distillation for Flow Matching Models

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

An Zhao, Shengyuan Zhang, Zhongjian Sun +5

College of Computer Science and Technology, Zhejiang University, Zhejiang, China · School of Software Technology, Zhejiang University, Zhejiang, China · Princeton University, Princeton, USA +1

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

Jun 9, 2026cs.LG

Exploring the Design Space of Reward Backpropagation for Flow Matching

Aligning text-to-image flow matching models with human preferences via direct reward backpropagation is sample-efficient but hampered by two well-known pathologies: activations cannot be stored across the full sampling trajectory at modern model scale, and chained Jacobian products across steps inflate the reward gradient as it travels back to early indices. Connector-based methods, such as LeapAlign, address these issues by replacing the full backward trajectory with a short pinned path, highlighting a useful decoupling between sampling and optimization. However, the quality of the resulting gradient depends on how accurately this short path approximates the full rollout, especially over long intervals. We propose FlowBP, a unified surrogate-trajectory framework that treats the backward trajectory itself as the design object. FlowBP keeps a no-gradient cached rollout for sampling, then builds a lightweight backward surrogate from cached and selectively re-forwarded velocities. This view separates four choices: the reward-model input, active set, integration weights, and bridge coupling, and recovers prior direct-gradient methods as particular settings. Within this framework, we instantiate three variants: FlowBP-Sparse uses sparse Euler reconstruction, FlowBP-Bridge adds controlled bridge coupling, and FlowBP-Lagrange raises the order of leap quadrature. All three bound memory by the active-set size and limit gradient chaining to at most one Jacobian factor. Across SD3.5-M, FLUX.1-dev, and FLUX.2-Klein-base on preference, quality, and compositional metrics, the three variants improve over direct-gradient baselines on most metrics.

Ruoyu Wang, Boye Niu, Xiangxin Zhou +3

1Westlake University · 2Tencent Hunyuan · University of Sydney +1

Flow Matching AI Alignment T2I Generation Flow-Based Generative Modeling

Jun 9, 2026cs.LG

Flow-DPPO: Divergence Proximal Policy Optimization for Flow Matching Models

Recent work has demonstrated that online reinforcement learning (RL) can substantially improve the quality and alignment of flow matching models for image and video generation. Methods such as Flow-GRPO and CPS cast the denoising process as a Markov Decision Process and apply PPO-style ratio clipping to enforce a trust region. However, we argue that ratio clipping is structurally ill-suited for flow models: the probability ratio between new and old policies is a noisy, single-sample estimate of the true policy divergence, leading to over-constraining in some regions of the trajectory and under-constraining in others. We propose Flow-DPPO (Flow Divergence Proximal Policy Optimization), which replaces ratio clipping with a divergence proximal constraint. A key observation is that the per-step policy in flow models is Gaussian, enabling exact and cheap computation of the KL divergence between old and new policies. Flow-DPPO employs an asymmetric divergence mask that blocks gradient updates only when they simultaneously move away from the trusted region and violate the divergence threshold. Experiments show that Flow-DPPO achieves higher rewards with better KL-proximal efficiency, alleviates catastrophic forgetting, promotes balanced multi-objective optimization, and enables stable multi-epoch training where ratio clipping degrades. Code and models are available at https://github.com/Tencent-Hunyuan/UniRL/tree/main/FlowDPPO.

Bowen Ping, Xiangxin Zhou, Penghui Qi +3

Xi’an Jiaotong University · Tencent Hunyuan · National University of Singapore

RL for Video Generation RL for Image Generation Proximal Policy Optimization Flow-Based Generative Modeling RL for Generative Models

Jun 9, 2026cs.LG

Flexible Flows for Biological Sequence Design

Designing functional biological sequences requires navigating vast discrete spaces under strict evolutionary and biophysical constraints. Discrete Flow Matching (DFM) offers a generative framework over such spaces, but existing approaches rely on biologically uninformative couplings and offer limited flexibility for variable-length sequence generation and fine-grained control. We propose a structured coupling that encodes domain-specific preferences among sequence elements, biasing the source distribution toward plausible regions without modifying the flow objective or training procedure. Building on this, we introduce a latent edit-based rate parameterization that models variable-length generation via edit operations conditioned on a shared global latent, akin to a latent variable model, while remaining tractable. We further introduce a latent classifier-free guidance mechanism that steers generation coherently in continuous latent space, along with Dirichlet-prior temperature scaling for test-time control over edit operations. Our method achieves state-of-the-art performance across diverse biological sequence tasks, including density estimation, unconditional and conditional DNA sequence generation, and peptide sequence generation.

Yogesh Verma, Dani Korpela, Harri Lähdesmäki +1

Aalto University, Finland · Aalto University and YaiYai Ltd

Flow Matching Molecular Generation Flow-Based Generative Modeling Conditional Generative Modeling Sequence Modeling Discrete Flow Matching

Jun 9, 2026cs.CV

Few-step Generative Models as Lossy Compression

DiffC provides a principled way to reuse pre-trained diffusion models for lossy compression, but its encoding and decoding procedures remain slow because they require many discretized forward and reverse steps. We study whether few-step generative models -- Rectified Flow, Consistency Trajectory Models (CTM), and MeanFlow -- can be cast as codecs within the same reverse channel coding (RCC) framework. The main challenge is that RCC requires posterior and shared distribution parameters, whereas these models do not explicitly parameterize intermediate conditional distributions. For Rectified Flow and MeanFlow, we use the equivalence between velocity parameterization and diffusion-style denoising parameterization to derive the quantities required by RCC. For CTM, which is distilled from EDM, we adopt the EDM noise parameterization together with local Gaussian approximations of the sender and shared distributions at intermediate states. This yields a proof-of-concept probabilistic formulation that enables compression with pre-trained few-step generative models without retraining. On low-resolution benchmarks, the resulting codecs reduce encoding and decoding time and improve realism in the low-bit-rate regime.

Fuma Kimishima, Jinjia Zhou

Hosei University, Tokyo, Japan

Learned Image Compression Flow-Based Generative Modeling Generative Image Compression

Jun 8, 2026cs.LG

Compositional Generative Modeling from Decentralized Data

Learning the compositional nature of the physical world requires joint observation of interacting factors. However, because practical data is often decentralized, these factors are fragmented across isolated silos. Existing decentralized generative approaches focus only on modeling the union of siloed data, overlooking novel combinations implied by the collective whole. To bridge this gap, we introduce Decentralized Compositional Flow Matching (DCFM), a framework that enforces structural constraints across the global set of generative factors, without exchanging any raw data. DCFM enables novel combinations to emerge through peer interactions, even when no single data source can independently support the composition. Empirically, DCFM substantially outperforms federated learning and mixture-of-experts baselines across conditional image generation, robotic spatial planning, and medical attribute co-occurrence modeling.

Mashrur M. Morshed, Vishnu Naresh Boddeti

Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA.

Flow Matching Decentralized Learning Generative Modeling Flow-Based Generative Modeling Compositional Representation Learning Conditional Generative Modeling+1

Jun 8, 2026cs.LG

A Theory on Flow Matching with Neural Networks

In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields. We establish convergence guarantees for gradient descent in the over-parameterized 2-layered ReLU neural network regime. We derive generalization bounds for the conditional velocity-field matching objective. Building on these results, we provide Wasserstein-distance guarantees for the samples generated by the induced flow. Our analysis is based on generalization bound for multi-task representation learning with unbounded losses, which may be of independent interest beyond flow-based generative modeling. These theoretical results are validated through extensive experiments on both synthetic and real-world image benchmarks.

Yihan He, Qishuo Yin, Yuan Cao +2

Princeton University, Princeton, NJ, USA. · The University of Hong Kong, Hong Kong. · Northwestern University, Evanston, IL, USA.

Neural Network Generalization Flow Matching Neural Network Optimization Flow-Based Generative Modeling Conditional Generative Modeling

Jun 7, 2026cs.CV

CSFlow: Aligning Flow Matching with Human Contrast Sensitivity

We introduce Contrast Sensitive Flow (CSFlow), a weighting scheme that connects the human eye's Contrast Sensitivity Function (CSF) to the iterative denoising steps of flow matching. Because real-world images concentrate signal at low spatial frequencies, these components reach high signal-to-noise ratio earlier during continuous diffusion than high-frequency components. When generating images with diffusion or flow matching models, this induces a soft autoregressive structure in Fourier space, where coarse image content stabilizes before fine detail. Meanwhile, the human visual system is unequally sensitive to spatial frequencies: very low and very high frequencies require significantly higher contrast to be perceived. We for the first time merge these observations through two contributions: (1) a metric that estimates which frequencies are generated at each reverse flow interval and (2) timestep weights obtained by aligning the frequencies generated at each noise level with human contrast sensitivity. We validate our contributions experimentally showing that these weights can improve generative performance by lowering FID by 4.7%, increasing Inception Score by 2.2% and improving GenEval scores by 2.5% using inference-only timestep modification or short fine-tuning. Qualitatively, we find that our CSFlow weights lead to better visual realism and less cartoonish appearance of generated images.

Malgorzata Galinska, Bart Pogodzinski, Jan Eric Lenssen

Max Planck Institute for Informatics, Saarland Informatics Campus

Flow Matching Diffusion-Based Image Generation Flow-Based Generative Modeling

Jun 7, 2026cs.CL

Continuous Language Diffusion as a Decoder-Interface Problem

Gaussian-corrupted sentence embeddings have no direct linguistic interpretation, yet continuous diffusion language models can generate fluent text from them. We study this puzzle through Embedded Language Flows (ELF) and identify a decoder-basin mechanism: our evidence suggests that denoising becomes reliable when trajectories reach regions where the native decoder can read stable tokens. We introduce a diagnostic protocol for denoisability, semantic recoverability, order sensitivity, decoder compatibility, and trajectory reliability. It exposes failures hidden by scalar metrics: low mean-squared error can discard linguistic content, low perplexity can reflect low-entropy collapse, and clean latent reconstruction can coexist with a narrow decoder basin. A decoder-margin bound explains why token recovery depends on margin and local decoder sensitivity, not latent error alone. Auditing public ELF checkpoints reveals an interface phase diagram: early predictions are weakly readable, mid-trajectory disagreement marks a competition region, and late predictions enter a high-margin decoder basin. Once inside, token realization is surprisingly simple on generated ELF states: frozen T5 (Text-to-Text Transfer Transformer) token-embedding lookup recovers

93

--

96\%

of native decoder decisions, and a single linear readout reaches

97.9\%

agreement at 32k samples, leaving an

\approx1.1

--

1.2

perplexity gap in a structured residual tail. Under conservative held-out gates, a margin rule exits roughly

17

--

28\%

earlier in denoising steps under an explicit diagnostic monitor. Boundary checks on LangFlow, BitstreamDiffusion, and the Continuous Latent Diffusion Language Model (Cola-DLM) show that the same interface questions remain meaningful when the state object and decoder change. Continuous and latent diffusion language models should therefore be evaluated as representation-decoder systems.

Zhicheng Du, Lan Ma

Tsinghua Shenzhen International Graduate School, Tsinghua University

Latent Diffusion Models Diffusion Language Model Decoding Flow-Based Generative Modeling Diffusion Language Models Continuous Diffusion Language Models

Jun 7, 2026cs.LG

Active Flow Expansion for Out-of-Distribution Discovery: from Theory to Molecules

Standard flow and diffusion pre-training matches the distribution of available data (e.g., molecules), which often covers only a small fraction of the valid design space. In generative discovery, however, one aims to sample valid new-to-nature designs, assigned negligible probability under, and thus inaccessible to, standard models fitted to the observed data. To overcome this limitation, we depart from data distribution matching and view a generative model through its generable set: the region it covers with non-negligible probability. This allows to introduce a new learning principle for out-of-distribution flow modeling: enlarging a model's generable set to increase coverage of the valid design space. We propose Active Flow Expansion (ActFlow), a continued pre-training method that employs verifier feedback to expand a pre-trained model over new valid regions by iteratively adapting to synthetic data generated through active exploration in the learned flow representation. Theoretically, we establish to our knowledge first-of-their-kind statistical learning guarantees for out-of-distribution flow modeling, analyzing generable set expansion as a local-to-global reachability process over a learned representation. Empirically, we assess ActFlow with suitable out-of-distribution generative modeling metrics across small organic molecules, mid-sized drug-like molecules, therapeutic peptides, and protein sequence design tasks. Results show that ActFlow expands valid coverage far beyond the region modeled by the initial pre-trained model, significantly outperforming widely adopted synthetic flow pre-training methods.

Riccardo De Santi, Bruce Lee, Cristian Perez Jensen +6

ETH Zurich ETH AI Center · University of Pennsylvania · Caltech FutureHouse

Synthetic Data Pretraining Normalizing Flows Generative Modeling Molecular Generation Flow-Based Generative Modeling

Jun 7, 2026cs.CV

Learning to Solve Generative ODEs Beyond the Linear Span

Diffusion and flow generative models sample by integrating a learned ODE, but high quality still requires many sequential model evaluations. Solver learning reduces this cost by adapting scalar coefficients, timesteps, or both, while keeping the backbone model fixed. In this work, we identify a structural bottleneck in this update family: each step remains span-limited. Since the scalar-coefficient update lies in the span of buffered velocity evaluations, it can fit only the in-span component while leaving any out-of-span residual unreachable by scalar recombination alone. We propose SpanLift, a lightweight neural solver that augments scalar-coefficient updates with a spatial residual operator. SpanLift keeps a fixed base solver as an in-span prior and learns a spatial residual operator over the state and velocity buffer. The operator is trained by endpoint teacher matching, preserves the pretrained backbone, and adds no model NFEs. Empirically, the learned correction transfers across base solvers and is predominantly out-of-span. Across pixel-space diffusion, latent flow matching, and precipitation nowcasting, SpanLift achieves state-of-the-art few-step sampling. With only 3 NFE, it improves CIFAR-10 FID from 8.16 to 5.69 and ImageNet FID from 17.37 to 11.83.

Sihyeon Kim, Seunghun Lee, Vikas Singh +1

Korea University · KAIST · University of Wisconsin–Madison

Few-Step Diffusion Sampling Flow-Based Generative Modeling Neural ODEs Diffusion Model Inference Acceleration

Jun 5, 2026cs.LG

Where Rectified Flows Leak: Characterising Membership Signals Along the Interpolation Path

Understanding what generative models retain from training data remains challenging, with implications for copyright and privacy. Beyond verbatim reproduction, models can encode subtler traces of their training data that never surface in their outputs yet remain exploitable. We study this regime for Rectified Flows, which are increasingly used in deployed generative systems. We analyse the interpolation path

X_λ= (1-λ)X_0 + λX_1

that defines the Rectified Flow training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over

λ

, wich accumulates during training, while the validation metrics remain stable. The signal has a maximum whose location we derive in closed form under Gaussian assumptions. We validate these predictions on both audio and images and show that the bell-shaped structure is universal, while the peak prediction holds when our assumptions are satisfied. As a proof of concept, we exploit this specific

λ

-resolved structure to perform a Membership Inference Attack, distinguishing members of the training set from non-members.

Thomas Sesmat, Gabriel Meseguer-Brocal, Geoffroy Peeters

LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France · Deezer Research, Paris, France

Data Leakage Rectified Flow Membership Inference Attacks Memorization in Generative Models Generative Modeling Flow-Based Generative Modeling

Jun 5, 2026cs.LG

GenPO++: Generative Policy Optimization with Jacobian-free Likelihood Ratios

Generative policies provide expressive and multimodal action distributions, making them attractive for reinforcement learning (RL) in complex continuous-control tasks. Among them, flow-based policies are especially appealing because they generate actions through deterministic transport maps. However, applying such generative policies to likelihood-based on-policy learning remains limited by the difficulty of evaluating the probability of executed actions. Existing flow RL methods either replace the true action-density ratio with approximate surrogates, which can introduce biased updates, or recover exact likelihoods through dummy-action augmentation, which enlarges the policy space and increases computation. In this work, we propose GenPO++, a reversible generative policy optimization framework that uses history states as auxiliary memory in a high-order reversible ODE solver, yielding exact inversion without changing the original action dimension. The resulting generative policy map has a log-determinant determined only by fixed solver coefficients, enabling exact and Jacobian-free likelihood-ratio computation. This design preserves the expressiveness of generative flow policies while avoiding both action ratio bias and dummy-action overhead. We evaluate GenPO++ on large-scale simulated control, fine-tuning, and real-world robotic manipulation tasks, where it achieves competitive or superior performance over state-of-the-art on-policy RL methods, while improving training stability and computational efficiency.

Ke Hu, Shutong Ding, Panxin Tao +2

ShanghaiTech University

RL Control Policy Gradient Methods Flow-Based Generative Modeling RL for Generative Models

Jun 4, 2026cs.LG

Your GFlowNet Secretly Learns an Optimal Transport Plan

Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph. In this work, we establish a theoretical connection between non-acyclic GFlowNets and optimal transport (OT). We show that fixing the initial flow distribution in a minimum-flow GFlowNet reduces its objective to a Kantorovich OT problem with graph-induced shortest path costs. At the optimum, the learned GFlowNet policy therefore encodes an optimal transport plan from the source distribution to the target distribution: we show that sampling trajectories from the minimum-flow GFlowNet recovers the corresponding optimal coupling. Our formulation enables applying the GFlowNet learning framework to OT problems on large graphs via edge flows and neural parameterization. Experiments confirm agreement with exact OT solvers and demonstrate that GFlowNets can learn high-quality transport plans.

Ian Maksimov, Nikita Morozov, Denis Belomestny +1

1HSE University · 2Duisburg-Essen University

Generative Flow Networks Flow-Based Generative Modeling Optimal Transport

Jun 4, 2026cs.SD

SB-RF: Schrödinger Bridge Rectified Flow for One-Step Robust Speech Enhancement

Generative models have shown promising results for speech enhancement (SE), but they often rely on multi-step inference, limiting low-latency deployment. We propose SB-RF, a one-step generative framework that integrates Rectified Flow (RF) with Schrödinger Bridge (SB) theory. During training, SB-RF samples intermediate states from an SB time marginal and trains a conditional velocity field with the RF velocity-matching objective. At inference, SB-RF starts from the noisy observation and applies a single Euler update. Experiments show that SB-RF achieves competitive performance among generative methods on the VoiceBank-DEMAND benchmark. To further assess performance beyond this standard setting, we evaluate SB-RF on a simulated low signal-to-noise ratio test set using an expanded training dataset. Under these conditions, SB-RF achieves superior performance over the compared baselines, supporting its potential for real-world applications.

Caixia Lu, Xueyang Lv, Penglong Hu +1

Rectified Flow Schrödinger Bridges One-Step Generative Modeling Speech Enhancement Flow-Based Generative Modeling Noise Robustness

Jun 3, 2026cs.RO

Potential-Guided Flow Matching for Vision-Language-Action Policy Improvement

Large vision-language-action (VLA) policies are increasingly trained as conditional generative models over action chunks. Yet deployment produces mixed-quality experience-successful demonstrations, partial completions, recoverable mistakes, and failures-that is difficult to use with standard imitation. Full behavior cloning (BC) imitates failures, filtered BC discards useful sub-trajectories, and offline reinforcement learning adds a large critic. We introduce ForesightFlow, a self-guided flow-matching policy that augments each generated action chunk with a learned success-potential trajectory. The same flow proposes and scores candidate actions, enabling best-of-

K

inference without an external critic. The key issue is that policy improvement and value calibration require different supervision: advantage weighting should emphasize high-quality actions, but applying the same weights to potential coordinates suppresses failure gradients and creates overconfident scores. We address this with decoupled advantage-weighted flow matching, applying exponentiated advantage weights only to action velocities while training potential velocities uniformly. We further derive a one-step boundary estimator for conditional flow matching, allowing advantage computation with a single stop-gradient forward pass. Across five BEHAVIOR-1K simulation tasks and five real-world bimanual tasks, ForesightFlow improves over imitation baselines, matches the strongest separate-critic baseline in simulation success, improves real-world success, and reduces training compute by

38\%

. Ablations show that decoupling prevents value hallucination, the one-step estimator preserves candidate-ranking fidelity, and self-guided sampling improves long-horizon execution.

Yunpeng Mei, Jiakai He, Hongjie Cao +12

1Beijing Institute of Technology · 2Tsinghua University · 3The Hong Kong University of Science and Technology (Guangzhou)

Flow Matching Visuomotor Policy Learning Vision-Language-Action Models Flow-Based Generative Modeling

Jun 3, 2026cs.CV

MeshFlow: Efficient Artistic Mesh Generation via MeshVAE and Flow-based Diffusion Transformer

We present MeshFlow, a new method for generating artist-like 3D meshes. Current mesh generators often adopt Auto-Regressive (AR) next-token prediction, a natural choice given the discrete nature of mesh topology. However, AR methods scale poorly because the inference cost is quadratic in mesh size. They also require discretizing the vertex coordinates, which introduces quantization errors. To address these challenges, we introduce a Variational Autoencoder (VAE) that, supervised with a contrastive loss, represents both continuous vertex positions and discrete connectivity in a continuous latent space. This latent space is significantly more compact than prior token-based mesh representations. We then build a 3D generator based on a Rectified Flow transformer, generating all mesh vertices and edges in parallel. Our model generates meshes 18x faster than the fastest AR generator while also achieving excellent accuracy across standard mesh-generation metrics. Homepage: https://mesh-flow.github.io/, Code: https://github.com/facebookresearch/meshflow

Weiyu Li, Antoine Toisoul, Tom Monnier +4

Meta AI · Hong Kong University of Science and Technology

3D Mesh Generation 3D Representation Learning Flow-Based Generative Modeling

Jun 2, 2026cs.GR

SymTRELLIS: Symmetry-Enforced Voxel Latents for 3D Generation

Single-view 3D generative models have achieved impressive visual quality, yet they are not designed to satisfy structural or functional requirements, and in practice, often fall short. Symmetry is one such requirement: violations, even subtle ones, on symmetry can render a model physically unusable. We present SymTRELLIS, a method that enforces arbitrary finite point group symmetries (rotational, reflectional, and polyhedral) during the flow-based 3D generation of TRELLIS.2, without retraining the underlying VAE or flow model. Our key idea is to approximate the latent-space action of spatial transformations as a learned linear operator on voxel latents, implemented as a lightweight spatial-transform latent mapper trained on generic, non-symmetric 3D data. At generation time, we enforce symmetry by averaging predicted flow velocities across all symmetry-equivalent transformations at each ODE step, a process we call velocity symmetrization. The symmetry specification can be estimated automatically from an initial TRELLIS.2 generation or supplied by the user, enabling deliberate fold manipulation beyond what the input image suggests. On a curated benchmark of 266 strictly symmetric objects spanning 2- to 20-fold rotations and polyhedral symmetry groups, SymTRELLIS substantially reduces all symmetry error metrics compared to TRELLIS.2, Hunyuan3D-2.1, and TripoSG, while maintaining reconstruction accuracy comparable to the base model.

Guangda Ji, Qimin Chen, Qinchan Li +3

Simon Fraser University, Burnaby, BC, Canada · ShanghaiTech University, Shanghai, China · Augmenta, Toronto, ON, Canada

3D Asset Generation Generative Modeling 3D Shape Generation Flow-Based Generative Modeling

Jun 2, 2026cs.CV

Optimal Transport Flow Matching by Design

Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution. When prior-data pairs are coupled via optimal transport (OT), the learned trajectories are straight and non-crossing, enabling fast, even single-step, generation. However, computing the OT coupling in high dimensions is intractable, and existing methods attempt to solve the OT problem, at the cost of persistent bias or significant overhead. Rather than solving for the OT coupling, we reformulate the problem. Once the prior is treated as a design choice rather than a fixed input, the OT coupling between prior and data is no longer unique. Many priors admit an OT-optimal identity coupling to the data, leaving us free to choose one that is also tractable to sample. We identify low-frequency projection of natural images as such a choice. The identity coupling between data and its low-frequency representation is empirically OT-optimal, the prior is structured enough to be sampled by a lightweight model at inference, and the remaining flow-matching task reduces to synthesizing high-frequency detail. Interpolating the prior with Gaussian noise further improves generation quality while preserving the OT coupling. The approach requires no modifications to the flow model itself, and integrates naturally with latent-space models, classifier-free guidance, and one-step generation frameworks. Across all benchmarks, our method reduces trajectory curvature by more than

2\times

compared to existing flow matching methods, yielding better generation quality in the few-step regime.

Shimon Malnick, Matan Rusanovsky, Ohad Fried +1

1Tel Aviv University · 2Reichman University

Flow Matching One-Step Generative Modeling Flow-Based Generative Modeling Optimal Transport

Jun 2, 2026cs.RO

Let the Dynamics Flow: Stable Flow Matching Dynamical Systems

Flow matching has recently emerged as a powerful approach for imitation learning, enabling scalable, expressive, and multimodal motion policies. However, when modeling these policies as dynamical systems, incorporating formal stability guarantees into these generative models is a prerequisite to ensure safe and generalizable robot behaviors, which remains a significant challenge. This paper introduces Stable Flow Matching Dynamical Systems (SFMDS), a novel framework that bridges the gap between highly expressive generative modeling and formal stability guarantees. SFMDS parametrizes dynamical systems via flow matching while constraining the model to satisfy positive invariance and/or Lyapunov stability conditions. We propose two variants: a soft constraint based on a penalty term, and a hard structural constraint embedded directly into the model architecture. We further extend both formulations to Lie groups to robustly handle orientation trajectories. Experiments on benchmark datasets, in simulation, and on a humanoid robot show that SFMDS learns stable, scalable, and multimodal dynamical systems in low- and high-dimensional state spaces, enabling safe and expressive robot motion generation. SFMDS matches or outperforms state-of-the-art methods on unimodal datasets, while substantially improving performance on multimodal datasets, where competing approaches fail to capture multi-modal behaviors. Accompanying source code and video are available at: https://let-the-dynamics-flow.github.io/SFMDS/.

Rodrigo Pérez-Dattari, Francisco Leiva, Andrea Testa +3

Department of Robotics, Perception, and Learning, KTH Royal Institute of Technology, Stockholm, Sweden. · Advanced Mining Technology Center (AMTC) and Department of Electrical Engineering, Universidad de Chile, Santiago, Chile. · Bosch Center for Artificial Intelligence, Renningen, Germany. +1

Flow Matching Lyapunov Stability Robot Motion Generation Robot Imitation Learning Flow-Based Generative Modeling

Jun 1, 2026cs.LG

Low-Pass Flow Matching

Flow Matching typically relies on white noise sources, a choice often misaligned with the power spectra of natural data, which tend to decay with frequency. To address this, we introduce Low-Pass Flow Matching, a variant of Flow Matching based on an operator-modulated interpolant. This formulation induces a time-varying spectral bias that transitions from the source spectrum to a frequency-decaying bias as the path approaches the data. We validate our method on unconditional image generation tasks, including the scientific Galaxy10 dataset. Empirically, we show that our method is particularly effective when paired with adaptive ODE solvers, where it improves or preserves sample quality while substantially reducing sampling cost compared to standard baselines.

Francesco M. Ruscio, T. Konstantin Rusch

ELLIS Institute Tübingen & · Max Planck Institute for Intelligent Systems & · AITHYRA +2

Flow Matching Image Generation Continuous Normalizing Flows Flow-Based Generative Modeling

May 31, 2026cs.AI

FlowTime: Towards Continuous Generative Watch Time Prediction via Flow-based Personalized Priors

Watch time has emerged as a pivotal metric for optimizing deep user engagement in short-video recommender systems. However, current methods of watch time prediction (WTP) suffer from inherent paradigm-specific limitations. Direct Regression faces mean-collapse due to unimodal Gaussian assumptions, while Ordinal Regression is hampered by quantization errors from rigid discretization. Similarly, Discrete Generative Regression struggles with high inference latency and heuristic vocabulary design. Beyond these specific flaws, a shared deficiency is the inability to capture the intrinsic multimodality and heterogeneity of User-Item Interaction Patterns. To address these challenges, we first revisit the WTP problem from a causal perspective and identify these user-specific patterns as structural confounders that modulate watch time outcomes, where identical interests manifest as distinct watch time outcomes conditioned on diverse user habits. Then, we formally propose a new (or the fourth) paradigm -- Continuous Generative Regression, and introduce FlowTime, a novel method utilizing a One-step Generative Variational Autoencoder. FlowTime effectively circumvents the latency of iterative denoising while maintaining the expressivity of continuous latent spaces. Furthermore, we design a Flow-based Personalized Prior that leverages NFs to warp a standard Gaussian prior into a complex, history-conditioned manifold, thereby enabling the adaptive modeling of multimodal interaction patterns. Finally, we build TimeRec, the first open-source WTP Library, alongside a novel personalization metric to establish a rigorous benchmarking standard. Extensive offline experiments and online A/B tests demonstrate FlowTime's significant superiority over SOTA methods.

Hongxu Ma, Han Zhou, Chenghou Jin +5

Fudan University Shanghai, China · Kuaishou Technology Beijing, China · Shanghai University of Finance and Economics Shanghai, China +1

Recommender Systems Flow-Based Generative Modeling Conditional Generative Modeling

May 31, 2026cs.LG

Strong Stochastic Flow Maps

Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation. Flow maps alleviate this problem by learning the solution map of the differential equation directly, enabling few-step sampling. Yet, current methods are restricted to approximating the solution map of ODEs. These methods can be used to learn the transition kernel of an SDE, thereby obtaining a solution map that recovers the marginal distributions of the process (weak convergence) rather than the solution path (strong convergence). We propose Strong Stochastic Flow Maps (SSFMs) as a novel framework for learning the strong solution map of additive-noise SDEs, directly generalizing deterministic flow maps to the stochastic setting. Further, a polynomial approximation to Brownian motion is introduced and shown to converge pathwise. These results enable a simulation-free training objective for the solution map of diffusion models. We demonstrate that SSFMs outperform previous stochastic flow map methods on image generation and enable few-step sampling of molecular systems.

Sam McCallum, Zander W. Blasingame, Timothy Herschell +3

University of Bath · 2AITHYRA

Stochastic Differential Equations Few-Step Diffusion Sampling Flow Map Learning Diffusion-Based Image Generation Flow-Based Generative Modeling

May 29, 2026cs.LG

Geometric Erasure by Contrastive Velocity Matching in Rectified Flows

While the rapid adoption of multimodal generative models offers immense potential, it has also increased the risks of harmful content synthesis, deepfakes, and copyright infringements. To address these challenges, concept erasure has emerged as a prospective safeguard. However, as the field gradually transitions from U-Net-based diffusion models to Rectified Flow Transformers, erasure research has struggled to keep pace. In this work, we introduce GEM, a simple but highly effective erasure framework for Rectified Flow models. As part of our contribution, we establish a principled bridge between trajectory-based unlearning grounded in Generative Flow Networks and classic teacher-guided erasure: we translate trajectory-based signals into a teacher-guided flow-matching setup that unifies the strengths of both paradigms. Concretely, a teacher provides complementary attraction and repulsion signals that we combine into a single geometric guidance objective, yielding targeted suppression of unwanted concepts while preserving benign generation.

Jonas Henry Grebe, Tobias Braun, Anna Rohrbach +1

Technical University of Darmstadt & hessian.AI, Germany.

Rectified Flow Flow-Based Generative Modeling Concept Erasure

May 28, 2026cs.LG

Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design

Adapting generative foundation models, in particular diffusion and flow models, to optimize given reward functions (e.g., binding affinity) while satisfying constraints (e.g., molecular synthesizability) is fundamental for their adoption in real-world scientific discovery applications such as molecular design or protein engineering. While recent works have introduced scalable methods for reward-guided fine-tuning of such models via reinforcement learning and control schemes, it remains an open problem how to algorithmically trade-off reward maximization and constraint satisfaction in a reliable and predictable manner. Motivated by this challenge, we first present a rigorous framework for Constrained Generative Optimization, which brings an optimization viewpoint to the introduced adaptation problem and retrieves the relevant task of constrained generation as a sub-case. Then, we introduce Constrained Flow Optimization (CFO), an algorithm that automatically and provably balances reward maximization and constraint satisfaction by reducing the original problem to sequential fine-tuning via established, scalable methods. We provide convergence guarantees for constrained generative optimization and constrained generation via CFO. Ultimately, we present an experimental evaluation of CFO on both synthetic, yet illustrative, settings, and a molecular design task. Across these evaluations, CFO achieves consistent increases in reward while ensuring high constraint satisfaction, showcasing its practical utility for constrained generative optimization.

Sven Gutjahr, Riccardo De Santi, Luca Schaufelberger +2

Department of Computer Science, ETH Zurich · ETH AI Center · NCCR Catalysis, Switzerland +1

Constrained Generative Modeling Molecular Optimization Generative Modeling Flow-Based Generative Modeling

May 28, 2026cs.LG

Midpoint Generative Models

We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the corresponding drift field vanishes at the midpoint time,

t=1/2

. We show that the norm of this field defines a valid discrepancy between distributions, which we call the Midpoint Divergence. We extend this discrepancy beyond the midpoint by introducing randomly flipped interpolations and further generalize it by replacing deterministic linear Flow Matching interpolations with symmetric stochastic interpolants, yielding a generalized Midpoint Divergence. Finally, we derive a variational formulation of our generalized divergence, yielding a tractable objective for training a one-step generator. The resulting MGM algorithm offers an effective and theoretically grounded approach to generative modeling, achieving competitive performance against existing one-step generative modeling methods.

Daniil Shlenskii, Nikita Gushchin, Lev Novitskiy +2

1AXXX, Russia · 2Applied AI Institute, Russia · 3Kandinsky Lab, Russia

Flow Matching Stochastic Interpolants One-Step Generative Modeling Flow-Based Generative Modeling

May 27, 2026cs.LG

Random Process Flow Matching: Generative Implicit Representations of Multivariate Random Fields

Generative modeling provides a powerful framework for learning data distributions. These models initially relied on probabilistic methods such as Gaussian Processes (GP) for uncertainty-aware predictions and shifted towards larger trainable models to learn more complex distributions. In this work, we introduce Random Process (RP) Flow, a Flow Matching-based framework that represents the vector field as a neural implicit function. Unlike modern generative methods, our setting involves a single observed field, from which only sparse measurements are available. RP Flow uses Random Fourier Features to learn an implicit signal representation that can be queried at any arbitrary location from a limited set of observations, while encoding uncertainty through ensemble sampling. We propose constructing a Bayesian posterior by GP regression in the source space to generate high-quality samples. Our empirical results demonstrate that this framework generates realistic samples along with calibrated uncertainty estimates, even under challenging conditions such as high frequency, high sparsity, or high dimensionality. These findings position RP Flow as a milestone towards generative models for reconstruction tasks where data is scarce and uncertainty must remain traceable.

Julien Lalanne, David Picard, Lionel Boillot +3

Navier, CNRS, Univ Gustave Eiffel, ENPC, IP Paris, France · TotalEnergies, OneTech, France · LIGM, CNRS, Univ Gustave Eiffel, ENPC, IP Paris, France

Flow Matching Uncertainty Quantification Generative Modeling Flow-Based Generative Modeling

May 27, 2026cs.LG

Parameter-Efficient Generative Modeling with Controlled Vector Fields

We introduce a continuous-time generative modeling framework, motivated by the Chow-Rashevskii theorem, that builds expressive flows from a small set of fixed vector fields and learned scalar controls. Instead of learning an unconstrained high-dimensional vector field, our framework constructs the velocity by modulating fixed vector fields with learned scalar control functions. When the fixed fields are bracket-generating, their Lie algebra spans the ambient space, providing a mechanism for expressive transport with only a small number of learned control channels and offering a parameter-efficient geometric alternative to standard vector-field parameterizations. This decoupled formulation yields a structured and interpretable generative model in which the number of learned scalar output channels can be chosen independently of the ambient dimension. We formulate an expressivity principle showing that, under suitable controllability and well-posedness assumptions, such controlled flows can transport a source distribution to a target distribution. We train the resulting model using a continuous-normalizing-flow likelihood objective and present proof-of-concept experiments on synthetic distributions.

Peyman Morteza

Generative Modeling Continuous Normalizing Flows Flow-Based Generative Modeling

May 26, 2026cs.LG

GenSBI: Generative Methods for Simulation-Based Inference in JAX

Flow and diffusion generative models have established themselves as widely adopted density estimators for simulation-based inference (SBI), extending naturally from neural posterior estimation to likelihood and joint density estimation. Their principled optimization objectives and freedom from architectural constraints have driven rapid adoption across the natural sciences. Yet the most widely used SBI libraries remain PyTorch-based, leaving researchers who develop their forward models and analysis pipelines in JAX without a native option. We present GenSBI, an open-source library that implements flow matching, score matching, and denoising diffusion entirely in JAX. The library offers three transformer-based architectures - SimFormer, Flux1, and a novel Flux1Joint that extends gate-modulated transformer blocks to joint density estimation - all interchangeable through a unified interface that decouples generative method, neural backbone, and inference mode. GenSBI provides an end-to-end workflow from training through posterior calibration (SBC, TARP, LC2ST) and supports custom architectures with domain-specific embedding networks. We validate the framework on standard SBI benchmarks, achieving near-ideal mean C2ST scores (0.50-0.56, where 0.50 is ideal) on SBIBM tasks with minimal per-task tuning and well-calibrated posterior coverage across all tested configurations. The code is publicly available at https://github.com/aurelio-amerio/GenSBI.

Aurelio Amerio

Instituto de Física Corpuscular (IFIC) Universitat de València & CSIC València, Spain

Flow Matching Simulation-Based Inference Neural Posterior Estimation Flow-Based Generative Modeling Score-Based Generative Modeling Diffusion Models

May 26, 2026cs.LG

Recursive Flow Matching

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20

\times

speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.

Jiahe Huang, Sihan Xu, Sharvaree Vadgama +1

University of California, San Diego · University of Michigan

Neural Surrogate Modeling Flow Matching One-Step Generative Modeling Flow-Based Generative Modeling Spatiotemporal Forecasting Physics-Based Simulation

May 25, 2026cs.LG

Two-Parameter Flows for Learning Population Dynamics of Physical Systems

This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only sampling-time transports from a base distribution to each marginal and then extract a physics-time velocity by regressing on coupled synthetic trajectories. We prove that the resulting physics-time dynamics are unique and inherit regularity from the sampling-time transports. Because we can build on standard, well-developed conditional flow matching techniques for learning the base-to-marginal transports, our approach scales to high dimensions and avoids per-step optimal-transport couplings, while allowing admissible non-gradient dynamics that can naturally explain rotational or circulating physics phenomena.

Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer

Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA.

Dynamical Systems Continuous Normalizing Flows Flow-Based Generative Modeling

May 25, 2026cs.LG

AdvantageFlow: Regularized Advantage-Weighted RL in Flow Models

We present AdvantageFlow, a forward-process reinforcement learning (RL) algorithm for rectified flow models. The algorithm minimizes an advantage-weighted prediction loss, which maximizes reward, regularized by the rollout policy, which convexifies the objective and makes its optimization stable. Our objective can be viewed as fitting a local reward-improving target distribution. The rollout regularization arises as a variance reduction step. We evaluate AdvantageFlow empirically on text-to-image generation with Stable Diffusion 3.5 Medium and FLUX.1, and compare it to both forward- and reverse-process RL algorithms.

Branislav Kveton, Anup Rao, Subhojyoti Mukherjee +2

Adobe Research

Rectified Flow RL for Image Generation Flow-Based Generative Modeling RL for Generative Models

May 22, 2026cs.CV

Flow-Based Generative Modeling for Optimizing Sampling Policies in Compressed Sensing Applications

Numerous modern applications in signal processing and medical imaging necessitate acquiring high-dimensional signals under tight resource constraints. Traditional sampling theory suggests that accurate signal reconstruction requires a number of measurements proportional to the signal's ambient dimension, a requirement often too expensive or impractical. Compressed sensing challenges this notion by demonstrating that sparse signals can be recovered with fewer measurements, provided the measurement operator meets certain conditions. This proof-of-concept study presents a task-aware flow-based generative framework -- a reformulation of the conventional Flow Matching training paradigm with a flow model trained to optimize subsampling in compressed sensing applications. We establish the fundamental feasibility of the proposed framework of learning subsampling masks that substantially enhance the performance of compressed sensing for image classification, image reconstruction, and MRI acceleration. For the image reconstruction task, our method demonstrated state-of-the-art performance, achieving Peak Signal-to-Noise Ratio of 25.17 dB at the subsampling rate of 5% on the CelebA dataset and 29.24 dB when reconstructing

8\times

accelerated MRI measurements (fastMRI dataset) with the minimal computational overhead. These results highlight the effectiveness of task-conditioning within generative flow models and reveal a promising direction for representation learning strategies. Overall, the proposed framework offers a unified, flexible approach to designing data- and task-driven sensing schemes that can be potentially adapted to a broad range of inverse problems.

Roman Pavelkin, Luis A. Zavala-Mondragon, Christiaan G. A. Viviers +1

Eindhoven University of Technology, Eindhoven

Flow Matching Image Reconstruction Accelerated MRI Reconstruction Adaptive Sampling Compressed Sensing Flow-Based Generative Modeling

May 22, 2026cs.RO

Sparse Compositional Flow Matching by geometric assembly from motion primitives

Embodied trajectories, such as the executable motion sequences of robotic manipulators, underwater vehicles, and mobile robots, are a fundamental output of embodied AI. Modern generative models often treat them as a dense, monolithic signal generated point by point, fitting an intricate high-dimensional posterior while leaving the data's latent structure unmodeled, the same sample inefficiency long identified by the structured generative model literature. We argue that a compositional latent structure is a natural choice: many embodied tasks share recurring motion fragments that can be made explicit as a finite repertoire of reusable motion primitives, and compositional units naturally align with subtask boundaries to support task decomposition. Existing compositional generators, however, compose in a latent space and rely on post-hoc decoding to relate sampled units to actual trajectory segments. We instead compose directly in the physical trajectory space through a flow-matching framework with two coupled designs. Motion-Primitive Dictionary Learning equips each atom with a learnable length mask and binary starting indicators so the atom itself is the primitive, reused verbatim wherever it is placed. Structural Sparse Flow Matching with Geometric Constraints then generates a binary placement matrix using duration-aware tokenization and a differentiable geometric loss that enforces spatial continuity and temporal contiguity where adjacent primitives meet. On Open X-Embodiment and 3DMoTraj, the framework attains state-of-the-art accuracy and reduces the FDE/ADE ratio from 1.8 to 1.07, improving ADE by 19.2% and FDE by 21.0% over the strongest baseline.

Yan Tang, Yuanbo Tang, Tingyu Cao +2

Tsinghua Shenzhen Graduate School, Tsinghua University, Shenzhen, China · School of AI, Chinese University of Hong Kong (Shenzhen)

Flow Matching Robot Motion Generation Flow-Based Generative Modeling

May 22, 2026cs.LG

PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient alternative to diffusion models, but practical implementations typically rely on a single finite-capacity global vector-field estimator. In such heterogeneous temporal distributions, distinct regimes may pass through nearby flow states while requiring incompatible conditional velocities. A monolithic estimator trained with the standard

\ell_2

velocity-matching objective may therefore learn an overly smoothed approximation of the local transport field. This estimator-level smoothing can attenuate branch-specific dynamics, leading to spectral distortion and poor mode coverage. To address this, we propose PrismFlow, a new FM method with Koopman-inspired dynamical experts. Each expert learns residual corrections in a latent space where local nonlinear temporal evolution can be approximated by linear transitions. We further propose a confidence-aware Winner-Take-All (WTA) objective that updates only the expert best aligned with each sample while masking gradients to the others, encouraging mode-specific specialization. During sampling, the selected expert adds a residual dynamical correction to the global transport field, preserving FM stability while recovering fine-grained and high-frequency temporal structures. Across various benchmarks, PrismFlow effectively mitigates the spectral contraction in standard FM and achieves state-of-the-art performance, with a 15.6% gain in Context-FID and a 38.6% improvement in Discriminative Score, while remaining robust in low-data settings and effective for forecasting and imputation.

Junru Zhang, Lang Feng, Jinbo Wang +6

Zhejiang University, China · Nanyang Technological University, Singapore · I2R, Agency for Science, Technology and Research (A*STAR), Singapore

Flow Matching Mixture of Experts Time Series Forecasting Time Series Generation Flow-Based Generative Modeling

May 20, 2026cs.AI

Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards

Inference-time guided sampling steers state-of-the-art diffusion and flow models without fine-tuning by interpreting the generation process as a controllable trajectory. This provides a simple and flexible way to inject external constraints (e.g., cost functions or pre-trained verifiers) for controlled generation. However, existing methods often fail when composing multiple constraints simultaneously, which leads to deviations from the true data manifold. In this work, we identify root causes of this off-manifold drift and find that the approximation error scales severely with gradient misalignment. Building on these findings, we propose Conflict-Aware Additive Guidance (

g^\text{car}

), a lightweight and learnable method, which actively rectifies off-manifold drift by dynamically detecting and resolving gradient conflicts. We validate

g^\text{car}

across diverse domains, ranging from synthetic datasets and image editing to generative decision-making for planning and control. Our results demonstrate that

g^\text{car}

effectively rectifies off-manifold drift, surpassing baselines in generation fidelity while using light compute. Code is available at https://github.com/yuxuehui/CAR-guidance.

Xuehui Yu, Fucheng Cai, Meiyi Wang +2

Smart Systems Institute, National University of Singapore, Singapore · Faculty of Computing, Harbin Institute of Technology, Harbin, China · School of Computing, National University of Singapore, Singapore

Constrained Generative Modeling Diffusion Model Guidance Generative Flow Networks Flow-Based Generative Modeling Inference-Time Guidance

May 19, 2026cs.CV

FullFlow: Upgrading Text-to-Image Flow Matching Models for Bidirectional Vision--Language Generation

Modern text-to-image diffusion models encode rich visual priors, but expose them only through one-way text-conditioned generation. Existing unified vision--language models derived from them recover bidirectional capability through large-scale joint pretraining or substantial retraining of the text pathway, discarding the strong image prior the text-to-image backbone already encodes. We introduce \emph{FullFlow}, a parameter-efficient recipe that upgrades a pretrained rectified-flow text-to-image model into a bidirectional vision--language generator by training only LoRA adapters and lightweight text heads. FullFlow keeps images in their native continuous flow and adds a discrete insertion process for text. Separate image and text timesteps turn inference into trajectory selection in a two-dimensional generative space, enabling text

\rightarrow

image, image

\rightarrow

text, joint sampling, and partial-text prediction with a single backbone. On Stable Diffusion 3 (SD3) under an identical trainable-parameter count and matched LoRA rank, FullFlow improves text

\rightarrow

image FID from

62.7

to

31.6

and image

\rightarrow

text CIDEr from

2.0

to

99.4

over a LoRA equivalent following the previous SOTA formulation (Dual Diffusion) at matched wall-clock training time, while reducing peak VRAM from

{\sim}84

,GB to

{\sim}38

,GB and raising throughput by

{\sim}8\times

on two RTX A5000 GPUs in under 24 hours, training only

{\sim}5\%

of the backbone parameters. The same recipe transfers to FLUX.1-dev and supports downstream VQA through partial-text generation. These results show that strong bidirectional vision--language capability can be unlocked from pretrained text-to-image flow models without full multimodal pretraining.

Eric Tillmann Bill, Enis Simsar, Alessio Tonioni +1

ETH Zurich · Google

Flow Matching Image Captioning Vision-Language Models VLM Adaptation Flow-Based Generative Modeling T2I Diffusion Models

May 19, 2026cs.CV

Probability-Conserving Flow Guidance

Diffusion and flow-based generative models dominate visual synthesis, with guidance aligning samples to user input and improving perceptual quality. However, Classifier-Free Guidance (CFG) and extrapolation-based methods are heuristic linear combinations of velocities/scores that ignore the generative manifold geometry, breaking probability conservation and driving samples off the learned manifold under strong guidance. We analyse guidance through the continuity equation and show its effect decomposes into a divergence term and a score-parallel term defined invariantly across parameterisations. We prove the divergence term blows up structurally as sampling approaches the data manifold, motivating a time-dependent schedule alongside score-parallel attenuation. The resulting plug-and-play rule, Adaptive Manifold Guidance (AdaMaG), bounds both terms at no additional inference cost. Finally, we show that most empirical heuristics for reducing saturation or improving generation quality correspond directly to the two terms in our decomposition. Across image generation benchmarks, AdaMaG improves realism, reduces hallucinations, and induces controlled desaturation in high-guidance regimes.

Parsa Esmati, Junha Hyung, Amirhossein Dadashzadeh +2

University of Bristol · KAIST

Diffusion Model Guidance Classifier-Free Guidance Generative Modeling Flow-Based Generative Modeling

May 19, 2026stat.ML

Tail Annealing for Heavy-Tailed Flow Matching

Standard generative models struggle with heavy-tailed data: Lipschitz architectures cannot produce power-law tails from Gaussian noise, and interpolating between heavy-tailed data and Gaussians is ill-posed. We propose a simple fix: apply the soft-log transform

φ(x) = \mathrm{sign}(x) \cdot \log(1 + |x|)

coordinate-wise to data before training, then exponentiate samples after generation. A Hill diagnostic decides per-coordinate whether to transform, leaving light-tailed margins untouched at no added complexity. This compresses heavy tails into a range where standard flow matching succeeds, without heavy-tailed base distributions or architectural modifications. We provide theoretical intuition for why this works: the log-transform maps Pareto tails to exponentials, and the induced dynamics implement a form of tail annealing via power transformations. On a 144-configuration multivariate benchmark (3 copulas,

d

up to 100, 4 tail indices), Log-FM dominates specialized baselines on

W_1

, CVaR

_{99}

, and extreme-quantile metrics, and is the only method with zero severe divergences across 2{,}880 runs.

Jean Pachebat

1CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, France.

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

May 19, 2026cs.CV

FlowErase-RL: Rethinking Concept Erasure as Reward Optimization in Flow Matching Models

Recent advances in flow matching models have significantly improved text-to-image generation quality, but also introduce growing safety risks due to the generation of harmful or undesirable content. Existing concept erasure methods are either inference-time interventions with limited effectiveness or rely on supervised fine-tuning (SFT), which requires precisely aligned data and struggles with scalability and multi-concept settings. In this paper, we propose \emph{FlowErase-RL}, the first GRPO-based framework for concept erasure in flow matching models. We reformulate concept erasure as a reward optimization problem and introduce a \textbf{dynamic dual-path reward mechanism} that jointly optimizes (i) a Concept Erasure (CE) reward to suppress target concepts and (ii) a Non-target Space (NS) reward to preserve generative fidelity. The two reward paths are adaptively balanced during training via a performance-driven switching strategy, enabling stable optimization without explicit supervision. Extensive experiments on nudity, object, and artistic style erasure demonstrate that our method achieves state-of-the-art erasure performance while maintaining strong image quality and semantic alignment. Moreover, it exhibits robust resistance to adversarial attacks and scales effectively to multi-concept scenarios. Our results establish a new paradigm for safe and controllable generation in flow matching models.

Yi Sun, Zhiqi Zhang, Xinhao Zhong +5

Harbin Institute of Technology, Shenzhen · Jilin University · Tsinghua Shenzhen International Graduate School, Tsinghua University +2

Flow Matching T2I Generation Safe T2I Generation Flow-Based Generative Modeling RL for Generative Models Concept Erasure

May 19, 2026cs.CV

Multi-Scale Generative Modeling with Heat Dissipation Flow Matching

Diffusion models are widely used in image generation, with most relying on noise-based corruption and denoising. A distinct branch instead uses blur as the main corruption, preserving better color budgets and multi-scale detail by providing multi-scale priors. However, blur-based models remain in SDE-based frameworks and are not integrated into ODE-based frameworks, such as Flow Matching (FM). Meanwhile, in the blur-based formulation, the classical inverse heat-dissipation (IHD) process faces an ill-posed challenge. Moreover, under the data-manifold assumption, regressing blurred images from high-dimensional noise (or velocity) space is also difficult. We propose Heat Dissipation Flow Matching (HDFM), which introduces a continuous blurred (heat-dissipation) process into FM to inject multi-scale priors. HDFM aligns an interpolated heat-dissipation path to address ill-posedness and adopts

x

-prediction to mitigate high-dimensional regression difficulty. Toy experiments and ablation studies show that HDFM consistently benefits from both blur and

x

-prediction. The performance of HDFM outperforms most baseline methods on all datasets.

Jun Ma, Hanquan Zhang, Yanjun Qin +2

Department of Systems Science, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China · School of Computer Science and Technology, Xinjiang University, Urumqi 830049, China · International Academic Center of Complex Systems, Beijing Normal University, Zhuhai 519087, China +1

Flow Matching Image Generation Generative Modeling Flow-Based Generative Modeling Diffusion Models

May 19, 2026cs.GR

Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes

This paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts the flow matching (FM) paradigm to a mesh-based, triangulation-agnostic setting. Theoretically, it proposes a specific noise distribution which is triangulation agnostic, to be used inside the FM model's denoising process. While noise distributions are usually trivial to devise for, e.g., images, devising a triangulation-agnostic distribution proves to be a much more difficult task. We formulate a mathematical definition of triangulation agnosticism of distributions, via their spectrum. We then show that a discretization of a specific Gaussian random field called a Matérn process holds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to the triangulation-agnostic setting by using a state-of-the-art approach for learning signals on meshes in the gradient domain -- PoissonNet -- as the denoiser. We conduct experiments on elaborate tasks such as sampling elastic rest states, and generating poses of humanoids. Our method is shown to be capable of producing highly realistic results for meshes of over one million triangles, significantly exceeding the state-of-the-art in quality and diversity.

Tianshu Kuai, Arman Maesumi, Daniel Ritchie +1

Université de Montréal & Mila, Canada · Brown University, USA

Flow Matching 3D Mesh Generation Generative Modeling Flow-Based Generative Modeling

May 19, 2026cs.CV

Distribution Matching Distillation without Fake Score Network

Distribution Matching Distillation (DMD) provides an effective distribution-level correction for few-step generation, while relying on an auxiliary fake-score network to track the evolving generative distribution. Recent work combines DMD-style objectives with flow-map generators to exploit both forward-divergence training and reverse-divergence correction. The fake-score estimator remains an additional component with memory and update overhead. In this work, we study whether this explicit tracker can be avoided when the generator itself has a flow-map structure. We propose Fake-Score-network-Free DMD (FSF-DMD), a DMD formulation for flow-map generators that replaces the auxiliary fake-score estimator with a generator-induced pseudo-velocity surrogate. The key observation is that the endpoint pseudo-velocity of a flow-map generator provides a tractable proxy for fake-velocity estimation, allowing the generator itself to supply the reverse-divergence signal. Building on this observation, we derive a practical objective, extend it with flow-map-consistent backward simulation, and introduce a self-teacher variant for training from scratch. In our ImageNet-1K

256 \times 256

experiments, FSF-DMD improves flow-map baselines, reaches lower FID than the listed DMD2 comparisons in the flow-map-initialized setting, and remains effective under flow-matching initialization and training from scratch.

Youngjoong Kim, Deokyeong Lee, Jaesik Park

Department of Computer Science and Engineering, Seoul National University · Department of Computer Science and Engineering, Sogang University Seoul, Republic of Korea

Diffusion Model Distillation Few-Step Diffusion Sampling Generative Flow Networks Flow-Based Generative Modeling Distribution Matching Distillation

May 18, 2026stat.ML

Flowing with Confidence

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run

k

ensembles or stochastic trajectories at

k\times

compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.

Friso de Kruiff, Dario Coscia, Max Welling +1

CuspAI · AMLab, University of Amsterdam · mathLab, SISSA

Flow Matching Uncertainty Quantification Image Generation Generative Modeling Flow-Based Generative Modeling

May 18, 2026cs.CV

SRC-Flow: Compact Semantic Representations Enable Normalizing Flows for Image Generation

Normalizing flows (NFs) provide exact likelihoods and deterministic invertible sampling, but have historically lagged behind diffusion models for large-scale image generation. We identify a key obstacle: NFs are required to learn a single invertible transport over the full ambient space, making them highly sensitive to high-dimensional representations. This leads to a semantic-capacity mismatch in modern visual representation spaces, where semantic information is compact but encoded in overcomplete features. We propose SRC-Flow, which introduces a Semantic Representation Compressor (SRC) to compact high-dimensional RAE features into a low-dimensional semantic space before flow modeling and preserve reconstruction through the frozen RAE decoder. This compact space reduces the modeling burden of NFs and enables effective likelihood-based generation in semantic representation space. We further adopt constant noise regularization tailored to the fixed unconditional bijection learned by flows. On ImageNet

256 \times 256

and

512 \times 512

, SRC-Flow achieves state-of-the-art generation quality among normalizing flow methods, with gFID scores of 1.65 and 2.07 under classifier-free guidance, while retaining exact likelihood computation in the compact semantic representation space and deterministic invertible sampling at the flow level. Codes and models will be available at https://github.com/longtaojiang/SRC-Flow.

Longtao Jiang, Jianmin Bao, Zhendong Wang +4

University of Science and Technology of China · Kling Team, Kuaishou Technology

Normalizing Flows Embedding Compression Flow-Based Generative Modeling

May 17, 2026astro-ph.IM

Accelerating Redshift-Conditioned Galaxy Image Synthesis with One-step Generative Modeling

Understanding galaxy morphology evolution across cosmic time requires models that can generate realistic galaxy populations conditioned on redshift. In this work, we study efficient redshift-conditioned generative modeling for astrophysical image synthesis using diffusion models and pixel-MeanFlow. We first review the connections between score-based diffusion models, Flow Matching, one-step generative models, and modern diffusion samplers. We then evaluate DDPM, DDIM, DEIS-AB2, DPM++2M, and one-step pixel-MeanFlow on the GalaxiesML-64 dataset using morphology-based metrics, including ellipticity, semi-major axis, Sérsic index, and isophotal area. Our results show a clear accuracy-efficiency trade-off: standard DDPM sampling achieves the best distributional fidelity but requires high computational cost, while second-order samplers substantially improve efficiency over DDIM. Pixel-MeanFlow enables single-step generation and achieves competitive performance on several morphology statistics, though it remains weaker than many-step DDPM for fine-grained structure. Our results demonstrate that one-step generative models can recover key galaxy morphology statistics at orders-of-magnitude lower computational cost, opening a path toward efficient conditional simulators for large cosmological surveys and simulation-based scientific inference.

Tianyue Yang, Sandro Tacchella, Xiao Xue

The Center for Computational Science University College London · Cavendish Laboratory Kavli Institute for Cosmology University of Cambridge

Conditional Image Generation One-Step Generative Modeling Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 17, 2026cs.LG

Drift Flow Matching

Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient one-step generation, but their direct generation paradigm limits such flexibility. In this work, we propose Drift Flow Matching (DFM), a framework that connects drifting generative modeling with flow-based iterative generation. DFM preserves the efficiency of direct transport maps while enabling generation to be refined through multiple inference steps when desired. This bridges the gap between one-step Drift Models and multi-step Flow Matching methods, and provides a novel generative paradigm that can adapt sampling computation to different quality--efficiency requirements. Extensive experiments across different tasks and datasets demonstrate the effectiveness and generality of the proposed framework.

Chenrui Ma, Xi Xiao, Lin Zhao +3

University of California, Irvine · University of Virginia · University of Alabama at Birmingham +1

Flow Matching Inference-Time Scaling One-Step Generative Modeling Flow-Based Generative Modeling Drifting Models

May 16, 2026cs.LG

Learning Unbiased Permutations via Flow Matching

Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a conditional flow matching framework that operates directly on the affine subspace of matrices with unit row and column sums. A closed-form tangent-space projector preserves these constraints exactly along every trajectory, by construction rather than through iterative correction, and a nearest-target coupling routes distinct noisy initializations toward distinct valid permutations. The result is a model that captures multimodal permutation distributions rather than collapsing them to a single mode. On a visual sorting task with blended-digit ambiguity and a symmetric linear assignment problem, PermFlow achieves high accuracy on unambiguous inputs and recovers both valid permutations under ambiguity, where Sinkhorn-based baselines structurally fail.

Yimeng Min, Carla P. Gomes

Department of Computer Science Cornell University Ithaca, NY, USA

Flow Matching Combinatorial Optimization Flow-Based Generative Modeling

May 16, 2026cs.CV

CAB: Accelerating Flow and Diffusion Sampling via Rectification and Corrected Adams-Bashforth

Flow and diffusion models achieve high-fidelity, high-resolution image synthesis, but often require many function evaluations (NFEs) at sampling time. Existing acceleration methods either require additional training through distillation or rely on training-free high-order solvers, and both can degrade sample quality at low NFE budgets. We propose CAB (Corrected Adams-Bashforth), a training-free sampler that accelerates both flow and diffusion models. CAB first transforms the sampling dynamics to a common rectified coordinate system, and then applies a multistep Adams-Bashforth predictor augmented with a simple correction term based on past velocity evaluations and therefore incurs no additional NFEs. The resulting method is simple, has the same algorithmic form across model classes, and has at least third-order local truncation error and second-order global error. Experiments on pretrained flow and diffusion models, including class-conditional and large-scale text-to-image benchmarks, show that CAB improves quality-NFE trade-offs in the low-step regime of 6-20 NFEs. It also remains competitive with strong training-free samplers at higher step counts across most tested models. The official implementation is available at https://github.com/Anuska-Roy/CAB.

Anuska Roy, Pravin Nair

Department of Electrical Engineering Indian Institute of Technology Madras, Chennai, India

Few-Step Diffusion Sampling Generative Flow Networks Diffusion-Based Image Generation Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 15, 2026cs.LG

Wavelet Flow Matching for Multi-Scale Physics Emulation

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions, while generative approaches better capture details but are costly. Latent-space generative models have emerged as a compromise but with the additional cost of separately pre-trained autoencoders. We propose Wavelet Flow Matching (WFM), a novel generative emulator that overcomes current trade-offs between cost and skill by performing optimal-transport directly in the multi-scale wavelet space. Rather than learning a latent compression, WFM leverages the hierarchical structure of a U-Net to jointly predict transport velocities of a prescribed wavelet representation. On three challenging systems of chaotic fluid dynamics, WFM achieves superior long-horizon stability, accuracy and spectral coherence compared to state-of-the-art models. Our results clearly position the wavelet space as an effective training-free representation for generative emulation of complex physical dynamics.

Gabriele Accarino, Juan Nathaniel, Carla Roesch +4

Department of Earth and Environmental Engineering Columbia University, NY, USA · University of Edinburgh Edinburgh, Scotland, UK · Courant Institute of Mathematical Sciences New York University, NY, USA +2

Flow Matching PDE Surrogate Modeling Wavelet Methods Generative Modeling Flow-Based Generative Modeling Computational Fluid Dynamics

May 15, 2026stat.ML

StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow

Diffusion and flow-based models are ubiquitously used for generative modelling and density estimation. They admit a deterministic probability flow ordinary differential equation (PF-ODE), analogous to continuous normalizing flows (CNFs), which describes the transport of the probability mass. Obtaining the likelihood from these models is of interest to many workflows, especially Bayesian analysis, and requires solving the trace of the Jacobian to compute the divergence of the learned PF-ODE, which is either

\mathcal{O}(D^2)

to compute exactly or

\mathcal{O}(D)

with a noisy estimate. We introduce StAD, a new distillation method to predict and learn the divergence of the PF-ODE using the Langevin-Stein operator without ever computing the Jacobian. We show that our method is competitive with the Hutchinson and Hutch++ on CIFAR-10, ImageNet and other density estimation tasks, consistently improving the variance and speed of the likelihood predictions compared to the Hutchinson. We additionally show our method will generalize to a varied class of generative models, and show that under some regularity conditions these learned vector fields can be made to satisfy the Stein class.

Gurjeet Jagwani, Stephen Thorp, Sinan Deger +1

Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Cambridge, UK · Research Computing Services, University of Cambridge, Cambridge, UK · Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, UK +1

Continuous Normalizing Flows Flow-Based Generative Modeling Density Estimation Diffusion Models

May 15, 2026cs.LG

Entropy Across the Bridge: Conditional-Marginal Discretization for Flow and Schrödinger Samplers

For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schrödinger bridges define probability paths, yet their inference grids are usually heuristic or inherited from one-endpoint diffusion. We derive a conditional-marginal entropy-rate objective for bridge-aware discretization, separating endpoint-conditioned bridge geometry from marginal flow evolution, and use it to build a training-free entropic inference-time scheduler from first principles. For Gaussian Brownian bridges this rate is closed-form and U-shaped, motivating boundary-heavy nonuniform grids. On trained two-dimensional bridge/flow models, the estimated profile recovers the predicted shape and improves 10-step ODE-Heun MMD over linear by 18.1%, with a paired 22.7% SDE-Heun improvement in the same low-NFE sweep. On EDM/CIFAR-10, the entropic time-discretization gives the best tested five-step FID (186.3 \pm 4.0 versus 200.5 \pm 2.9 for linear and 238.0 \pm 5.3 for cosine). On AlphaFlow protein generation, entropic conditional-marginal (cond-marg) scheduling shows advantage in low-NFE regimes on both CAMEO22 and ATLAS benchmarks. These results support entropy-rate scheduling as a practical low-budget allocation signal for high-dimensional bridge and flow samplers.

Bruno Trentini, Dejan Stancevic, Michael M. Bronstein +2

NVIDIA Corporation, Santa Clara, CA, USA · University of Oxford, Dept. of Computer Science, Oxford, UK · Donders Institute for Brain, Cognition, and Behaviour, Radboud University, Nijmegen, NL +1

Flow Matching Schrödinger Bridges Few-Step Diffusion Sampling Adaptive Sampling Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 14, 2026cs.CV

Aligning Latent Geometry for Spherical Flow Matching in Image Generation

Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

Tuna Han Salih Meral, Kaan Oktay, Hidir Yesiltepe +2

Virginia Tech · fal

Flow Matching Neural Representation Geometry Conditional Image Generation Image Generation Flow-Based Generative Modeling

May 14, 2026cs.CV

EverAnimate: Minute-Scale Human Animation via Latent Flow Restoration

We propose EverAnimate, an efficient post-training method for long-horizon animated video generation that preserves visual quality and character identity. Long-form animation remains challenging because highly dynamic human motion must be synthesized against relatively static environments, making chunk-based generation prone to accumulated drift: (i) low-level quality drift, such as progressive degradation of static backgrounds, and (ii) high-level semantic drift, such as inconsistent character identity and view-dependent attributes. To address this issue, EverAnimate restores drifted flow trajectories by anchoring generation to a persistent latent context memory, consisting of two complementary mechanisms. (i) Persistent Latent Propagation maintains a context memory across chunks to propagate identity and motion in latent space while mitigating temporal forgetting. (ii) Restorative Flow Matching introduces an implicit restoration objective during sampling through velocity adjustment, improving within-chunk fidelity. With only lightweight LoRA tuning, EverAnimate outperforms state-of-the-art long-animation methods in both short- and long-horizon settings: at 10 seconds, it improves PSNR/SSIM by 8%/7% and reduces LPIPS/FID by 22%/11%; at 90 seconds, the gains increase to 15%/15% and 32%/27%, respectively.

Wuyang Li, Yang Gao, Mariam Hassan +4

Flow Matching Long-Horizon Video Generation Memory-Augmented Video Generation Human Motion Generation Flow-Based Generative Modeling Temporal Consistency in Video Generation

May 14, 2026cs.CV

The Velocity Deficit: Initial Energy Injection for Flow Matching

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

Linze Li, Zong-Wei Hong, Shen Zhang +4

Jiiov Technology, Beijing, China.

Flow Matching Image Generation Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 13, 2026cs.CV

AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation

Few-step video generation has been significantly advanced by consistency distillation. However, the performance of consistency-distilled models often degrades as more sampling steps are allocated at test time, limiting their effectiveness for any-step video diffusion. This limitation arises because consistency distillation replaces the original probability-flow ODE trajectory with a consistency-sampling trajectory, weakening the desirable test-time scaling behavior of ODE sampling. To address this limitation, we introduce AnyFlow, the first any-step video diffusion distillation framework based on flow maps. Instead of distilling a model for only a few fixed sampling steps, AnyFlow optimizes the full ODE sampling trajectory. To this end, we shift the distillation target from endpoint consistency mapping

(z_{t}\rightarrow z_{0})

to flow-map transition learning

(z_{t}\rightarrow z_{r})

over arbitrary time intervals. We further propose Flow Map Backward Simulation, which decomposes a full Euler rollout into shortcut flow-map transitions, enabling efficient on-policy distillation that reduces test-time errors (i.e., discretization error in few-step sampling and exposure bias in causal generation). Extensive experiments across both bidirectional and causal architectures, at scales ranging from 1.3B to 14B parameters, demonstrate that AnyFlow achieves performance matches or surpasses consistency-based counterparts in the few-step regime, while scaling with sampling step budgets.

Yuchao Gu, Guian Fang, Yuxin Jiang +4

1NVIDIA · 2Show Lab, National University of Singapore · 3MIT

Video Diffusion Models Diffusion Model Distillation Few-Step Diffusion Sampling Video Generation Flow-Based Generative Modeling

May 13, 2026cs.LG

Sampling from Flow Language Models via Marginal-Conditioned Bridges

Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion models: each block of the denoising mean is a posterior marginal distribution over the clean token at that position. Standard DDPM-style samplers collapse these marginals to a single conditional-mean endpoint and bridge toward this simplex-valued point, which is generally not a valid one-hot sequence. We argue that the natural sampler for an FLM is instead posterior-predictive. At each reverse step, we sample a clean one-hot endpoint from the factorized posterior defined by the FLM token marginals, and then sample the next continuous state from the analytic Ornstein--Uhlenbeck bridge conditioned on that endpoint. The method is training-free, uses the same model evaluations as standard sampling, and gives a principled interface for token-level decoding controls such as temperature scaling and nucleus truncation. We show that, under exact posterior marginals, the endpoint approximation error is exactly the conditional multi-information among token positions. The induced one-step bridge kernel preserves all token-wise posterior-predictive marginals and loses only the residual cross-position dependence. Finally, we prove a Girsanov path-space comparison showing that the marginal-conditioned bridge has a no-larger denoising-error term than the frozen conditional-mean bridge, with strict improvement whenever intermediate coordinate-wise bridge observations reveal additional information about the clean token. Experiments with FLMs show that the sampler improves the quality--diversity tradeoff. Code is available at: github.com/imbirik/mcb.

Iskander Azangulov, Leo Zhang

Department of Statistics, University of Oxford

Flow Matching Language Model Decoding Language Modeling Flow-Based Generative Modeling

May 13, 2026cs.LG

Path-independent Flow Matching for Multi-parameter Generative Dynamics

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples.

Francisco Téllez, AmirHossein Zamani, Philippe Martin +5

Université de Montréal, Mila · Concordia University, Mila · Concordia University +2

Flow Matching Flow Map Learning Generative Modeling Flow-Based Generative Modeling Optimal Transport