Flow-Based Generative Modeling

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66 papers in the last four weeks, up 288% on the four weeks before. 0.6% of all new papers.

Jul 13Week of Sep 28

Latest papers 331

Jun 13, 2026cs.LG

PHINN: Persistent Homology Inspired Neural Network for Rare-Event Time Series Generation

Rare events in time series are critical to model but hard to learn due to data scarcity. Current generative models struggle with extreme values. We observe that rare events leave distinct topological fingerprints - transitions in Betti numbers from point-cloud embeddings - that are more stable and discriminative than statistical moments. We introduce PHINN, a flow-matching framework using dynamic Betti curves as conditioning signals and a persistence landscape loss for homology consistency. It scales to multivariate data, includes a natural-language interface to set Betti targets, supports cross-domain meta-learning and few-shot generation, and provides certified adversarial robustness. On financial, epidemiological, and multi-modal benchmarks, PHINN outperforms statistical and diffusion baselines in topological fidelity (beta-RMSE down 41-63%, transition accuracy up 84%) and matches jump-diffusion models in tail coverage while exceeding them in shape fidelity. All results have 95% confidence intervals.

Emre Yusuf, Ren Takahashi, Jayabrata Bhaduri

Defense.Codes (a DBA of CapaCloud Corp

Time Series Generation Flow-Based Generative Modeling Persistent Homology Conditional Generative Modeling

Jun 13, 2026cs.LG

Reward Transport: Property Control in Flow Matching via Noise-Space Alignment

The coupling in flow matching -- the rule pairing noise vectors with data points -- is typically treated as a computational choice. We show that this coupling can instead serve as an alignment interface: by matching noise and data according to a target molecular property, it embeds controllable structure directly into the learned flow field. Building on this view, we introduce Reward Transport, which uses optimal transport coupling at training time to align a scalar noise-space coordinate with molecular rewards; at inference, varying this coordinate steers the generated distribution without requiring an oracle, reward model, gradient guidance, or additional computation. In the coupling-preserving limit, thresholding this coordinate recovers the Cross-Entropy Method's truncated reward distribution, providing a principled, continuously adjustable distribution-level control knob. Empirically, on ZINC-250K and GuacaMol, sweeping the scalar induces monotone control of logP and consistent QED control over its operating range; most tellingly, the same knob produces opposite structural responses for different targets, growing molecules for logP but shrinking them for QED, which rules out a generic size bias. The interface is complementary to classifier-free guidance and conditional flow matching, while a negative result under epsilon-prediction diffusion clarifies where coupling-level alignment is structurally absent. Code: https://github.com/KehanGuo2/reward-transport

Kehan Guo, Yili Shen, Yujun Zhou +4

University of Notre Dame · Carnegie Mellon University

Flow Matching Molecular Optimization Molecular Generation Flow-Based Generative Modeling

Jun 12, 2026cs.LG

Emyx: Fast and efficient all-atom protein generation

Computational enzyme design requires generating proteins that scaffold catalytic residues and ligands, a task that demands both geometric accuracy and structural diversity from the underlying generative model. Current all-atom generators inherit expensive architectures from structure prediction, leading to high training costs and limited sample diversity. We argue that much of this complexity is unnecessary for generators, which condition on sparse geometric constraints rather than rich co-evolutionary signals. Emyx is a 140M-parameter conditional flow matching model that concentrates capacity within standard transformer blocks, replacing heavy embedding stacks with lightweight conditional representations and sparse connectivity. We additionally derive an exact reparametrisation of the flow matching interpolant into the EDM noise-level framework, bridging flow matching training efficiency with state-of-the-art sampling methods designed for diffusion models without retraining. Despite being the smallest model, Emyx outperforms both Proteína-Complexa and RFdiffusion3 against the AME enzyme design benchmark across success rate under strict evaluation requiring both global fold recovery and catalytic geometry accuracy, structural novelty, scaffold diversity, and geometric validity, while training in just

682

GPU-hours, roughly

4\times

less than RFdiffusion3.

Nicholas J. Williams, Ward Haddadin, Matteo P. Ferla +6

Xyme, Oxford, UK

Conditional Flow Matching 3D Molecular Generation Flow-Based Generative Modeling Protein Design

Jun 12, 2026cs.SD

Mask, Sample, Revise: A Revisable CTMC Inference Stack for Guided Discrete Flow Matching Text-to-Speech

Recent alignment-free non-autoregressive (NAR) text-to-speech (TTS) models formulate synthesis as a conditional infilling task, bypassing explicit duration predictors and external aligners. When speech is represented with neural codec tokens, the infilling problem becomes discrete, making Discrete Flow Matching (DFM), a Continuous-Time Markov Chain (CTMC) framework for discrete generation, a natural fit. However, inference-time control for stable low-step conditional infilling remains underexplored. We propose Mask, Sample, Revise, an inference-time CTMC stack for alignment-free DFM-TTS. The stack combines predictor-free guidance to strengthen text conditioning, prompt-matched conditional coupling to align the probability path with the acoustic prompt, and SC-ReMask, a schedule-constrained remasking mechanism that introduces token-to-mask transitions so de-masking decisions can be revised. These components require no post-hoc fine-tuning and operate in a single tau-leaping sampler. Controlled ablations show that this stack improves intelligibility and robustness in the low-NFE prompted setting, outperforming unguided and guidance-only samplers with substantially more steps.

Alef Iury Siqueira Ferreira, Lucas Rafael Stefanel Gris, Luiz Fernando de Araújo Vidal +4

Federal University of Goi´as, Goiˆania, Brazil · Federal University of Mato Grosso, Cuiab´a, Brazil · Elsa Speak, S˜ao Paulo, Brazil

Flow Matching TTS Synthesis Flow-Based Generative Modeling Inference-Time Guidance Discrete Flow Matching

Jun 11, 2026cs.CV

Surflo: Consistent 3D Surface Flow Model with Global State

Geometry is invariant to viewpoint, which makes any collection of images a redundant encoding of a single 3D state. Existing feed-forward reconstruction models fail to exploit this: per-view methods emit overlapping, unaligned pointmaps that grow linearly with input count, while global-latent methods commit to a fixed, low-resolution output. We introduce Surflo, which compresses a variable number of unposed RGB views into K latent tokens-one global state-and decodes oriented 3D surface points by independently transporting them from noise onto the surface via flow matching. This frees the output from any fixed grid or token budget: the same latent yields from a few thousand to a million points in a single forward pass. To suppress the local inconsistencies inherent to independent per-point decoding, an inference-time guidance term correlates nearby points by injecting a photometric gradient during ODE integration. Surflo matches or surpasses feed-forward baselines on surface metrics, runs an order of magnitude faster than optimization-based methods that require hundreds of views, and is the only feed-forward approach to combine a global latent with arbitrary-resolution decoding.

Antoine Guédon, Shu Nakamura, Nicolas Dufour +3

LIX, École polytechnique · Kyoto University · Kyutai +1

3D Reconstruction Multi-View 3D Reconstruction Flow-Based Generative Modeling Feed-Forward 3D Reconstruction

Jun 11, 2026cs.LG

PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Update

While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on https://github.com/MJianM/PolyFlow.

Jianming Ma, Qiyue Yang, Yang Zhang +4

Shanghai Jiao Tong University, Shanghai, China · Shanghai Innovation Institute, Shanghai, China

Constrained Generative Modeling Flow Matching Generative Modeling Safe Motion Planning Flow-Based Generative Modeling

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