Flow-Based Generative Modeling

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Overview

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

Latest papers

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

May 1, 2026

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

Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or propagate approximate covariance through many integration steps, trading off training cost, inference cost, or accuracy. We show that none of these trade-offs is necessary. By extending Tweedie's formula from the denoising setting to the flow matching interpolant, we derive an exact, closed-form expression for the posterior covariance at every point along the generative trajectory. The result depends on a single quantity, namely the divergence of the learned velocity field, which can be computed post-hoc on any pre-trained flow matching model, requiring no retraining and no architectural modification. For one-step generators such as MeanFlow, the same formula yields the end-to-end generation uncertainty in a single forward pass, eliminating the multi-step variance propagation required by all prior methods. Experiments on MNIST confirm that the resulting per-pixel uncertainty maps are semantically meaningful, concentrating on digit boundaries where inter-sample variation is highest, and that the scalar uncertainty score tracks actual prediction error, all at roughly 104×10^4 \times less total compute than ensembling or Monte Carlo dropout.

Jiarui Xing, Song Wang, Jian Wang

Yale University · Harvard Medical School

Flow MatchingUncertainty QuantificationBayesian InferenceFlow-Based Generative ModelingCovariance EstimationUncertainty Propagation
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May 1, 2026

Binomial flows: Denoising and flow matching for discrete ordinal data

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

Yair Shenfeld, Ricardo Baptista, Stefano Peluchetti

Flow MatchingFlow-Based Generative ModelingDiffusion ModelsDiscrete Flow Matching
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Apr 30, 2026

A unified perspective on fine-tuning and sampling with diffusion and flow models

We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward fine-tuning of pre-trained models. This problem can be approached from a stochastic optimal control (SOC) perspective, using adjoint-based or score matching methods, or from a non-equilibrium thermodynamics perspective. We provide a unified framework encompassing these approaches and make three main contributions: (i) bias-variance decompositions revealing that Adjoint Matching/Sampling and Novel Score Matching have finite gradient variance, while Target and Conditional Score Matching do not; (ii) norm bounds on the lean adjoint ODE that theoretically support the effectiveness of adjoint-based methods; and (iii) adaptations of the CMCD and NETS loss functions, along with novel Crooks and Jarzynski identities, to the exponential tilting setting. We validate our analysis with reward fine-tuning experiments on Stable Diffusion 1.5 and 3.

Carles Domingo-Enrich, Yuanqi Du, Michael S. Albergo

Microsoft Research New England · Harvard University, Kempner Institute

Stochastic Optimal ControlDiffusion SamplingDiffusion Model Fine-TuningFlow-Based Generative ModelingScore-Based Generative Modeling
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Apr 29, 2026

How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance

In generative modeling, we often wish to produce samples that maximize a user-specified reward such as aesthetic quality or alignment with human preferences, a problem known as guidance. Despite their widespread use, existing guidance methods either require expensive multi-particle, many-step schemes or rely on poorly understood approximations. We reformulate guidance as a deterministic optimal control problem, yielding a hierarchy of algorithms that subsumes existing approaches at the coarsest level. We show that the flow map, an object of significant recent interest for its role in fast inference, arises naturally in the optimal solution. Based on this observation, we propose Flow Map Reward Guidance (FMRG): a training-free, single-trajectory framework that uses the flow map to both integrate and guide the flow. At text-to-image scale, FMRG matches or surpasses baselines across inverse problems and reward-guided generation with as few as 3 NFEs, giving at least an order-of-magnitude speedup in comparison to prior state of the art. Code is available at https://github.com/jrrhuang/fmrg.

Jerry Y. Huang, Justin Lin, Sheel Shah +2

Carnegie Mellon University

Generative ModelingFlow-Based Generative ModelingConditional Generative Modeling
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Apr 28, 2026

FlowS: One-Step Motion Prediction via Local Transport Conditioning

Generative motion prediction must satisfy three simultaneous requirements for real-world autonomy: high accuracy, diverse multimodal futures, and strictly bounded latency. Diffusion models meet the first two but violate the third, requiring tens to hundreds of denoising steps. We identify a conditioning strategy that resolves this tension: single-step integration is accurate when the underlying transport problem is local. A model that must both discover the correct behavioral mode and traverse a long displacement in one step accumulates large discretization errors; conditioning the base distribution to lie near plausible futures reduces the problem to short-range refinement, the regime where a single Euler step suffices. We instantiate this local transport conditioning in FlowS, a conditional flow matching framework with two mechanisms. First, an online, scene-conditioned learned prior emits KK calibrated anchor trajectories per agent, each already near a plausible future, converting mode discovery into local correction. Second, a step-consistent displacement field enforces semigroup self-consistency, guaranteeing that a single step inherits multi-step accuracy. Crucially, anchoring this field at learned priors along straight-line paths yields a {stable, low-variance} training target, unlike prior self-consistency methods that suffer from {high-variance bootstrap} signals on curved diffusion paths. On the Waymo Open Motion Dataset, FlowS achieves state-of-the-art Soft mAP {(0.4804) and mAP (0.4703) with ensemble at 75,FPS} with single-step inference, demonstrating that local transport conditioning makes one-step generative motion prediction practical for safety-critical autonomy. Code and pretrained models will be released upon acceptance.

Leandro Di Bella, Adrian Munteanu, Bruno Cornelis

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

Flow MatchingTrajectory GenerationMulti-Agent Trajectory PredictionAutonomous Driving PerceptionOne-Step Generative ModelingFlow-Based Generative Modeling+2
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Apr 27, 2026

CoreFlow: Low-Rank Matrix Generative Models

Learning matrix-valued distributions from high-dimensional and possibly incomplete training data is challenging: ambient-space generative modeling is computationally expensive and statistically fragile when the matrix dimension is large but the sample size is limited. We propose CoreFlow, a geometry-preserving low-rank flow model that learns shared row/column subspaces across the matrix distribution, and then trains a continuous normalizing flow only on the induced low-dimensional core. CoreFlow is designed for settings where shared low-rank matrix geometry is present, especially in high-dimensional limited-sample regimes. This separates shared matrix geometry from sample-specific variation, preserves matrix structure, and substantially improves training efficiency. The same framework also handles incomplete training matrices through masked Riemannian updates and iterative completion. Across real and synthetic benchmarks, CoreFlow substantially improves spectral and moment-level generation quality in few-sample regimes while remaining competitive in data-rich settings, even under compression to 9% of the ambient dimension and with up to 40% missing training entries.

Dongze Wu, Linglingzhi Zhu, Yao Xie

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA

Generative ModelingContinuous Normalizing FlowsFlow-Based Generative ModelingMatrix Completion
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Apr 26, 2026

FlowPlace: Flow Matching for Chip Placement

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

Peng Xie, Ke Xue, Yunqi Shi +6

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

Constrained Generative ModelingFlow MatchingElectronic Design AutomationGenerative ModelingFlow-Based Generative Modeling
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Apr 25, 2026

MotionHiFlow: Text-to-motion via hierarchical flow matching

Text-to-motion generation aims to generate 3D human motions that are tightly aligned with the input text while remaining physically plausible and rich in fine-grained detail. Although recent approaches can produce complex and natural movements, they usually operate at only one temporal scale, which limits both semantic alignment and temporal coherence. Inspired by the fact that complex motions are conceptualized hierarchically rather than at a single temporal scale in the human cognitive system, we propose MotionHiFlow, a hierarchical flow matching framework to generate motion progressively by constructing flow path from low to high temporal scales. The flows at lower scales capture high-level semantics and coarse motion structures, while flows at higher scales refine temporal details. To link the flows across scales, we introduce a novel cross-scale transition process, ensuring continuity and preserving noise consistency. Furthermore, by integrating a Text-Motion Diffusion Transformer and a topology-aware Motion VAE, MotionHiFlow explicitly models structural dependencies among joints via joint-aware positional encoding and skeletal topology, enabling precise semantic alignment alongside fine-grained motion details. Extensive experiments on HumanML3D and KIT-ML benchmarks demonstrate state-of-the-art performance, with ablation studies confirming the effectiveness of the hierarchical design and key components. Code is available at https://github.com/ai-lh/MotionHiFlow.

Heng Li, Xiaotong Lin, Ling-An Zeng +3

Sun Yat-sen University · Shandong University · Guangdong Province Key Laboratory of Information Security Technology, China +1

Flow MatchingText-to-Motion GenerationHuman Motion GenerationFlow-Based Generative Modeling
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Apr 21, 2026

Normalizing Flows with Iterative Denoising

Normalizing Flows (NFs) are a classical family of likelihood-based methods that have received revived attention. Recent efforts such as TARFlow have shown that NFs are capable of achieving promising performance on image modeling tasks, making them viable alternatives to other methods such as diffusion models. In this work, we further advance the state of Normalizing Flow generative models by introducing iterative TARFlow (iTARFlow). Unlike diffusion models, iTARFlow maintains a fully end-to-end, likelihood-based objective during training. During sampling, it performs autoregressive generation followed by an iterative denoising procedure inspired by diffusion-style methods. Through extensive experiments, we show that iTARFlow achieves competitive performance across ImageNet resolutions of 64, 128, and 256 pixels, demonstrating its potential as a strong generative model and advancing the frontier of Normalizing Flows. In addition, we analyze the characteristic artifacts produced by iTARFlow, offering insights that may shed light on future improvements. Code is available at https://github.com/apple/ml-itarflow.

Tianrong Chen, Jiatao Gu, David Berthelot +2

Apple Machine Learning Research.

Normalizing FlowsAutoregressive Image GenerationFlow-Based Generative Modeling
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Apr 21, 2026

Frequency-Forcing: From Scaling-as-Time to Soft Frequency Guidance

While standard flow-matching models transport noise to data uniformly, incorporating an explicit generation order - specifically, establishing coarse, low-frequency structure before fine detail - has proven highly effective for synthesizing natural images. Two recent works offer distinct paradigms for this. K-Flow imposes a hard frequency constraint by reinterpreting a frequency scaling variable as flow time, running the trajectory inside a transformed amplitude space. Latent Forcing provides a soft ordering mechanism by coupling the pixel flow with an auxiliary semantic latent flow via asynchronous time schedules, leaving the pixel interpolation path itself untouched. Viewed from the angle of improving pixel generation, we observe that forcing - guiding generation with an earlier-maturing auxiliary stream - offers a highly compatible route to scale-ordered generation without rewriting the core flow coordinate. Building on this, we propose Frequency-Forcing, which realizes K-Flow's frequency ordering through Latent Forcing's soft mechanism: a standard pixel flow is guided by an auxiliary low-frequency stream that matures earlier in time. Unlike Latent Forcing, whose scratchpad relies on a heavy pretrained encoder (e.g., DINO), our frequency scratchpad is derived from the data itself via a lightweight learnable wavelet packet transform. We term this a self-forcing signal, which avoids external dependencies while learning a basis better adapted to data statistics than the fixed bases used in hard frequency flows. On ImageNet-256, Frequency-Forcing consistently improves FID over strong pixel- and latent-space baselines, and naturally composes with a semantic stream to yield further gains. This illustrates that forcing-based scale ordering is a versatile, path-preserving alternative to hard frequency flows.

Weitao Du

DAMO Academy

Flow MatchingImage GenerationFlow-Based Generative Modeling
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Apr 19, 2026

Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics

We introduce Prior-Fitted Functional Flows, a generative foundation model for pharmacokinetics that enables zero-shot population synthesis and individual forecasting without manual parameter tuning. We learn functional vector fields, explicitly conditioned on the sparse, irregular data of an entire study population. This enables the generation of coherent virtual cohorts as well as forecasting of partially observed patient trajectories with calibrated uncertainty. We construct a new open-access literature corpus to inform our priors, and demonstrate state-of-the-art predictive accuracy on extensive real-world datasets.

César Ojeda, Niklas Hartung, Wilhelm Huisinga +6

University of Potsdam, Germany · Technical University Berlin, Germany · Freie Universität Berlin, Germany +2

Probabilistic Time Series ForecastingHealthcareSynthetic Data GenerationZero-Shot Time Series ForecastingContinuous Normalizing FlowsPrior-Data Fitted Networks+2
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Apr 19, 2026

FlowC2S: Flowing from Current to Succeeding Frames for Fast and Memory-Efficient Video Continuation

This paper introduces a novel methodology for generating fast and memory-efficient video continuations. Our method, dubbed FlowC2S, fine-tunes a pre-trained text-to-video flow model to learn a vector field between the current and succeeding video chunks. Two design choices are key. First, we introduce inherent optimal couplings, utilizing temporally adjacent video chunks during training as a practical proxy for true optimal couplings, resulting in straighter flows. Second, we incorporate target inversion, injecting the inverted latent of the target chunk into the input representation to strengthen correspondences and improve visual fidelity. By flowing directly from current to succeeding frames, instead of the common combination of current frames with noise to generate a video continuation, we reduce the dimensionality of the model input by a factor of two. The proposed method, fine-tuned from LTXV and Wan, surpasses the state-of-the-art scores across quantitative evaluations with FID and FVD, with as few as five neural function evaluations.

Hovhannes Margaryan, Quentin Bammey, Christian Sandor

Team ARAI, Universit´e Paris-Saclay, CNRS, LISN, France · LTCI, T´el´ecom Paris, Institut Polytechnique de Paris, France

Flow MatchingT2V GenerationLong Video GenerationVideo GenerationVideo PredictionFlow-Based Generative Modeling
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Apr 17, 2026

The Amazing Stability of Flow Matching

The success of deep generative models in generating high-quality and diverse samples is often attributed to particular architectures and large training datasets. In this paper, we investigate the impact of these factors on the quality and diversity of samples generated by flow-matching models. Surprisingly, in our experiments on CelebA-HQ dataset, flow matching remains stable even when pruning 50% of the dataset. That is, the quality and diversity of generated samples are preserved. Moreover, pruning impacts the latent representation only slightly, that is, samples generated by models trained on the full and pruned dataset map to visually similar outputs for a given seed. We observe similar stability when changing the architecture or training configuration, such that the latent representation is maintained under these changes as well. Our results quantify just how strong this stability can be in practice, and help explain the reliability of flow-matching models under various perturbations.

Rania Briq, Michael Kamp, Ohad Fried +2

Forschungszentrum Jülich · TU Dortmund · Lamarr Institute +4

Flow MatchingGenerative ModelingFlow-Based Generative Modeling
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Apr 16, 2026

Frequency-Aware Flow Matching for High-Quality Image Generation

Flow matching models have emerged as a powerful framework for realistic image generation by learning to reverse a corruption process that progressively adds Gaussian noise. However, because noise is injected in the latent domain, its impact on different frequency components is non-uniform. As a result, during inference, flow matching models tend to generate low-frequency components (global structure) in the early stages, while high-frequency components (fine details) emerge only later in the reverse process. Building on this insight, we propose Frequency-Aware Flow Matching (FreqFlow), a novel approach that explicitly incorporates frequency-aware conditioning into the flow matching framework via time-dependent adaptive weighting. We introduce a two-branch architecture: (1) a frequency branch that separately processes low- and high-frequency components to capture global structure and refine textures and edges, and (2) a spatial branch that synthesizes images in the latent domain, guided by the frequency branch's output. By explicitly integrating frequency information into the generation process, FreqFlow ensures that both large-scale coherence and fine-grained details are effectively modeled low-frequency conditioning reinforces global structure, while high-frequency conditioning enhances texture fidelity and detail sharpness. On the class-conditional ImageNet-256 generation benchmark, our method achieves state-of-the-art performance with an FID of 1.38, surpassing the prior diffusion model DiT and flow matching model SiT by 0.79 and 0.58 FID, respectively. Code is available at https://github.com/OliverRensu/FreqFlow.

Sucheng Ren, Qihang Yu, Ju He +3

Johns Hopkins University · ByteDance

Flow MatchingConditional Image GenerationImage GenerationFlow-Based Generative Modeling
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Apr 16, 2026

One-Shot Generative Flows: Existence and Obstructions

We study dynamic measure transport for generative modeling, focusing on transport maps that connect a source measure P0P_0 to a target measure P1P_1 by integrating a velocity field of the form vt(x)=E[X˙t∣Xt=x]v_t(x) = \mathbb{E}[\dot X_t \mid X_t = x], where X∙=(Xt)tX_\bullet = (X_t)_t is a stochastic process satisfying (X0,X1)∼P0⊗P1(X_0,X_1)\sim{P_0}\otimes{P_1} and X˙t\dot X_t is its time derivative. We investigate when X∙X_\bullet induces a straight-line flow: a flow whose pointwise acceleration vanishes and is therefore exactly integrable by any first-order method. First, we develop multiple characterizations of straight-line flows in terms of PDEs involving the conditional statistics of the process. Then, we prove that straight-line flows under endpoint independence exhibit a sharp dichotomy. On the one hand, we construct explicit, computable straight-line processes for arbitrary Gaussian endpoints. On the other hand, we show that straight-line processes do not exist for targets with sufficiently well-separated modes. We demonstrate this obstruction through a sequence of increasingly general impossibility theorems that uncover a fundamental relationship between the sample-path behavior of a process with independent endpoints and the space-time geometry of this process' flow map. Taken together, these results provide a structural theory of when straight-line generative flows can, and cannot, exist.

Panos Tsimpos, Daniel Sharp, Youssef Marzouk

Operations Research Center · Massachusetts Institute of Technology · Cambridge, MA 02139 +2

Flow MatchingOne-Step Generative ModelingFlow-Based Generative ModelingOptimal Transport
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Apr 16, 2026

LeapAlign: Post-Training Flow Matching Models at Any Generation Step by Building Two-Step Trajectories

This paper focuses on the alignment of flow matching models with human preferences. A promising way is fine-tuning by directly backpropagating reward gradients through the differentiable generation process of flow matching. However, backpropagating through long trajectories results in prohibitive memory costs and gradient explosion. Therefore, direct-gradient methods struggle to update early generation steps, which are crucial for determining the global structure of the final image. To address this issue, we introduce LeapAlign, a fine-tuning method that reduces computational cost and enables direct gradient propagation from reward to early generation steps. Specifically, we shorten the long trajectory into only two steps by designing two consecutive leaps, each skipping multiple ODE sampling steps and predicting future latents in a single step. By randomizing the start and end timesteps of the leaps, LeapAlign leads to efficient and stable model updates at any generation step. To better use such shortened trajectories, we assign higher training weights to those that are more consistent with the long generation path. To further enhance gradient stability, we reduce the weights of gradient terms with large magnitude, instead of completely removing them as done in previous works. When fine-tuning the Flux model, LeapAlign consistently outperforms state-of-the-art GRPO-based and direct-gradient methods across various metrics, achieving superior image quality and image-text alignment.

Zhanhao Liang, Tao Yang, Jie Wu +2

1The Australian National University · 2ByteDance Seed

Diffusion Model AlignmentFlow MatchingImage GenerationDiffusion Model Fine-TuningFlow-Based Generative Modeling
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Apr 16, 2026

Towards Faster Language Model Inference Using Mixture-of-Experts Flow Matching

Flow matching retains the generation quality of diffusion models while enabling substantially faster inference, making it a compelling paradigm for generative modeling. However, when applied to language modeling, it exhibits fundamental limitations in representing complex latent distributions with irregular geometries, such as anisotropy and multimodality. To address these challenges, we propose a mixture-of-experts flow matching (MoE-FM) framework, which captures complex global transport geometries in latent space by decomposing them into locally specialized vector fields. Building on MoE-FM, we develop a non-autoregressive (NAR) language modeling approach, named YAN, instantiated with both Transformer and Mamba architectures. Across multiple downstream tasks, YAN achieves generation quality on par with both autoregressive (AR) and diffusion-based NAR language models, while requiring as few as three sampling steps. This yields a 40×40\times speedup over AR baselines and up to a 103×10^3\times speedup over diffusion language models, demonstrating substantial efficiency advantages for language modeling.

Aihua Li

Duke University

Non-Autoregressive Text GenerationFlow MatchingDiffusion Language Model InferenceFlow-Based Generative ModelingEfficient Language Model Inference
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Apr 15, 2026

PRiMeFlow: Capturing Complex Expression Heterogeneity in Perturbation Response Modelling

Predicting the effects of perturbations in-silico on cell state can identify drivers of cell behavior at scale and accelerate drug discovery. However, modeling challenges remain due to the inherent heterogeneity of single cell gene expression and the complex, latent gene dependencies. Here, we present PRiMeFlow, an end-to-end flow matching based approach to directly model the effects of genetic and small molecule perturbations in the gene expression space. The distribution-fitting approach taken by PRiMeFlow enables it to accurately approximate the empirical distribution of single-cell gene expression, which we demonstrate through extensive benchmarking inside PerturBench. Through ablation studies, we also validate important model design choices such as operating in gene expression space and parameterizing the velocity field with a U-Net architecture. Finally, by scaling PRiMeFlow to a broad perturbation data atlas spanning multiple datasets and employing a carefully designed pretraining-finetuning strategy, we demonstrate its outstanding performance on the H1 human embryonic stem cells from the ARC Virtual Cell Challenge benchmark.

Zichao Yan, Yan Wu, Mica Xu Ji +10

Altos Labs · Current affiliation: Verge Genomics · Current affiliation: Loka +1

Single-Cell Perturbation ModelingSingle-Cell TranscriptomicsFlow-Based Generative ModelingFlow Matching
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Apr 15, 2026

EMGFlow: Robust and Efficient Surface Electromyography Synthesis via Flow Matching

Deep learning-based surface electromyography (sEMG) gesture recognition is frequently bottlenecked by data scarcity and limited subject diversity. While synthetic data generation via Generative Adversarial Networks (GANs) and diffusion models has emerged as a promising augmentation strategy, these approaches often face challenges regarding training stability or inference efficiency. To bridge this gap, we propose EMGFlow, a conditional sEMG generation framework. To the best of our knowledge, this is the first study to investigate the application of Flow Matching (FM) and continuous-time generative modeling in the sEMG domain. To validate EMGFlow across three benchmark sEMG datasets, we employ a unified evaluation protocol integrating feature-based fidelity, distributional geometry, and downstream utility. Extensive evaluations show that EMGFlow outperforms conventional augmentation and GAN baselines, and provides stronger standalone utility than the diffusion baselines considered here under the train-on-synthetic test-on-real (TSTR) protocol. Furthermore, by optimizing generation dynamics through advanced numerical solvers and targeted time sampling, EMGFlow achieves improved quality-efficiency trade-offs. Taken together, these results suggest that Flow Matching is a promising and efficient paradigm for addressing data bottlenecks in myoelectric control systems. Our code is available at: https://github.com/Open-EXG/EMGFlow.

Boxuan Jiang, Chenyun Dai, Can Han

School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

Synthetic Data AugmentationConditional Generative ModelingFlow-Based Generative ModelingFlow Matching
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Apr 14, 2026

PianoFlow: Music-Aware Streaming Piano Motion Generation with Bimanual Coordination

Audio-driven bimanual piano motion generation requires precise modeling of complex musical structures and dynamic cross-hand coordination. However, existing methods often rely on acoustic-only representations lacking symbolic priors, employ inflexible interaction mechanisms, and are limited to computationally expensive short-sequence generation. To address these limitations, we propose PianoFlow, a flow-matching framework for precise and coordinated bimanual piano motion synthesis. Our approach strategically leverages MIDI as a privileged modality during training, distilling these structured musical priors to achieve deep semantic understanding while maintaining audio-only inference. Furthermore, we introduce an asymmetric role-gated interaction module to explicitly capture dynamic cross-hand coordination through role-aware attention and temporal gating. To enable real-time streaming generation for arbitrarily long sequences, we design an autoregressive flow continuation scheme that ensures seamless cross-chunk temporal coherence. Extensive experiments on the PianoMotion10M dataset demonstrate that PianoFlow achieves superior quantitative and qualitative performance, while accelerating inference by over 9\times compared to previous methods.

Xuan Wang, Kai Ruan, Jiayi Han +2

Zhejiang University Hangzhou, Zhejiang, China · Renmin University of China Beijing, China · Beijing Forestry University Beijing, China +1

Human Motion GenerationFlow-Based Generative Modeling
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Apr 14, 2026

SubFlow: Sub-mode Conditioned Flow Matching for Diverse One-Step Generation

Flow matching has emerged as a powerful generative framework, with recent few-step methods achieving remarkable inference acceleration. However, we identify a critical yet overlooked limitation: these models suffer from severe diversity degradation, concentrating samples on dominant modes while neglecting rare but valid variations of the target distribution. We trace this degradation to averaging distortion: when trained with MSE objectives, class-conditional flows learn a frequency-weighted mean over intra-class sub-modes, causing the model to over-represent high-density modes while systematically neglecting low-density ones. To address this, we propose SubFlow, Sub-mode Conditioned Flow Matching, which eliminates averaging distortion by decomposing each class into fine-grained sub-modes via semantic clustering and conditioning the flow on sub-mode indices. Each conditioned sub-distribution is approximately unimodal, so the learned flow accurately targets individual modes with no averaging distortion, restoring full mode coverage in a single inference step. Crucially, SubFlow is entirely plug-and-play: it integrates seamlessly into existing one-step models such as MeanFlow and Shortcut Models without any architectural modifications. Extensive experiments on ImageNet-256 demonstrate that SubFlow yields substantial gains in generation diversity (Recall) while maintaining competitive image quality (FID), confirming its broad applicability across different one-step generation frameworks. Project page: https://yexionglin.github.io/subflow.

Yexiong Lin, Jia Shi, Shanshan Ye +3

Sydney AI Centre, The University of Sydney, Sydney, NSW, Australia · School of Artificial Intelligence, Xidian University, Xi’an, Shaanxi, China · Australian Artificial Intelligence Institute, University of Technology Sydney, Sydney, NSW, Australia +1

Flow MatchingFlow-Based Generative ModelingOne-Step Generative ModelingConditional Generative ModelingMode Collapse
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Apr 13, 2026

MorphoFlow: Sparse-Supervised Generative Shape Modeling with Adaptive Latent Relevance

Statistical shape modeling (SSM) is central to population level analysis of anatomical variability, yet most existing approaches rely on densely annotated segmentations and fixed latent representations. These requirements limit scalability and reduce flexibility when modeling complex anatomical variation. We introduce MorphoFlow, a sparse supervised generative shape modeling framework that learns compact probabilistic shape representations directly from sparse surface annotations. MorphoFlow integrates neural implicit shape representations with an autodecoder formulation and autoregressive normalizing flows to learn an expressive probabilistic density over the latent shape space. The neural implicit representation enables resolution-agnostic modeling of 3D anatomy, while the autodecoder formulation supports direct optimization of per-instance latent codes under sparse supervision. The autoregressive flow captures the distribution of latent anatomical variability providing a tractable, likelihood-based generative model of shapes. To promote compact and structured latent representations, we incorporate adaptive latent relevance weighting through sparsity-inducing priors, enabling the model to regulate the contribution of individual latent dimensions according to their relevance to the underlying anatomical variation while preserving generative expressivity. The resulting latent space supports uncertainty quantification and anatomically plausible shape synthesis without manual latent dimensionality tuning. Evaluation on publicly available lumbar vertebrae and femur datasets demonstrates accurate high-resolution reconstruction from sparse inputs and recovery of structured modes of anatomical variation consistent with population level trends.

Mokshagna Sai Teja Karanam, Tushar Kataria, Shireen Elhabian

Kahlert School of Computing, Scientific Computing and Imaging Institute, University of Utah, Utah, USA

Statistical Shape Modeling3D Shape GenerationFlow-Based Generative Modeling
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Apr 13, 2026

LayerCache: Exploiting Layer-wise Velocity Heterogeneity for Efficient Flow Matching Inference

Flow Matching models achieve state-of-the-art image generation quality but incur substantial inference cost due to iterative denoising through large Transformer networks. We observe that different layer groups within a Transformer exhibit markedly heterogeneous velocity dynamics: shallow layers are highly stable and amenable to aggressive caching, while deep layers undergo large velocity changes that demand full computation. Existing caching methods, however, treat the entire Transformer as a monolithic unit, applying a single caching decision per timestep and thus failing to exploit this heterogeneity. Based on this finding, we propose LayerCache, a layer-aware caching framework that partitions the Transformer into layer groups and makes independent, per-group caching decisions at each denoising step. LayerCache introduces an adaptive JVP span K selection mechanism that leverages per-group stability measurements to balance estimation accuracy and computational savings. We formulate a three-dimensional scheduling problem over timesteps, layer groups, and JVP span, and solve it with a greedy budget allocation algorithm. On Qwen-Image (1024x1024, 50 steps), LayerCache achieves PSNR 37.46 dB (+5.38 dB over MeanCache), SSIM 0.9834, and LPIPS 0.0178 (a 70% reduction over MeanCache) at 1.37x speedup, dominating all prior caching methods on the quality-speed Pareto frontier.

Guandong Li

iFLYTEK

Flow MatchingFlow-Based Generative ModelingDiffusion Transformer
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Apr 13, 2026

Continuous Adversarial Flow Models

We propose continuous adversarial flow models, a type of continuous-time flow model trained with an adversarial objective. Unlike flow matching, which uses a fixed mean-squared-error criterion, our approach introduces a learned discriminator to guide training. This change in objective induces a different generalized distribution, which empirically produces samples that are better aligned with the target data distribution. Our method is primarily proposed for post-training existing flow-matching models, although it can also train models from scratch. On the ImageNet 256px generation task, our post-training substantially improves the guidance-free FID of latent-space SiT from 8.26 to 3.63 and of pixel-space JiT from 7.17 to 3.57. It also improves guided generation, reducing FID from 2.06 to 1.53 for SiT and from 1.86 to 1.80 for JiT. We further evaluate our approach on text-to-image generation, where it achieves improved results on both the GenEval and DPG benchmarks.

Shanchuan Lin, Ceyuan Yang, Zhijie Lin +2

ByteDance Seed

Flow-Based Generative ModelingImage Generation
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Apr 13, 2026

Probabilistic Prediction of Neural Dynamics via Autoregressive Flow Matching

Forecasting neural activity in response to naturalistic stimuli remains a key challenge for understanding brain dynamics and enabling downstream neurotechnological applications. Here, we introduce a generative forecasting framework for modeling neural dynamics based on autoregressive flow matching (AFM). Building on recent advances in transport-based generative modeling, our approach probabilistically predicts neural responses at scale from multimodal sensory input. Specifically, we learn the conditional distribution of future neural activity given past neural dynamics and concurrent sensory input, explicitly modeling neural activity as a temporally evolving process in which future states depend on recent neural history. We evaluate our framework on the Algonauts project 2025 challenge functional magnetic resonance imaging dataset using subject-specific models. AFM significantly outperforms both a non-autoregressive flow-matching baseline and the official challenge general linear model baseline in predicting short-term parcel-wise blood oxygenation level-dependent (BOLD) activity, demonstrating improved generalization and widespread cortical prediction performance. Ablation analyses show that access to past BOLD dynamics is a dominant driver of performance, while autoregressive factorization yields consistent, modest gains under short-horizon, context-rich conditions. Together, these findings position autoregressive flow-based generative modeling as an effective approach for short-term probabilistic forecasting of neural dynamics with promising applications in closed-loop neurotechnology.

Nicole Rogalla, Yuzhen Qin, Mario Senden +2

Department of Machine Learning and Neural Computing, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, the Netherlands · Department of Cognitive Neuroscience, Maastricht University, Maastricht, the Netherlands · Maastricht Brain Imaging Center, Maastricht University, Maastricht, the Netherlands

Functional Magnetic Resonance ImagingProbabilistic Time Series ForecastingConditional Generative ModelingFlow-Based Generative Modeling
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Apr 13, 2026

FlowCoMotion: Text-to-Motion Generation via Token-Latent Flow Modeling

Text-to-motion generation is driven by learning motion representations for semantic alignment with language. Existing methods rely on either continuous or discrete motion representations. However, continuous representations entangle semantics with dynamics, while discrete representations lose fine-grained motion details. In this context, we propose FlowCoMotion, a novel motion generation framework that unifies both treatments from a modeling perspective. Specifically, FlowCoMotion employs token-latent coupling to capture both semantic content and high-fidelity motion details. In the latent branch, we apply multi-view distillation to regularize the continuous latent space, while in the token branch we use discrete temporal resolution quantization to extract high-level semantic cues. The motion latent is then obtained by combining the representations from the two branches through a token-latent coupling network. Subsequently, a velocity field is predicted based on the textual conditions. An ODE solver integrates this velocity field from a simple prior, thereby guiding the sample to the potential state of the target motion. Extensive experiments show that FlowCoMotion achieves competitive performance on text-to-motion benchmarks, including HumanML3D and SnapMoGen.

Dawei Guan, Di Yang, Chengjie Jin +1

School of Artificial Intelligence and Data Science, University of Science and Technology of China · Suzhou Institute for Advanced Research, University of Science and Technology of China

Text-to-Motion GenerationHuman Motion GenerationMotion Representation LearningFlow-Based Generative Modeling
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Apr 10, 2026

MixFlow: Mixed Source Distributions Improve Rectified Flows

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of high curvature, as shown by previous work, is independence between the source distribution (standard Gaussian) and the data distribution. In this work, we tackle this limitation by two complementary contributions. First, we attempt to break away from the standard Gaussian assumption by introducing κ-FCκ\texttt{-FC}, a general formulation that conditions the source distribution on an arbitrary signal κκ that aligns it better with the data distribution. Then, we present MixFlow, a simple but effective training strategy that reduces the generative path curvatures and considerably improves sampling efficiency. MixFlow trains a flow model on linear mixtures of a fixed unconditional distribution and a κ-FCκ\texttt{-FC}-based distribution. This simple mixture improves the alignment between the source and data, provides better generation quality with less required sampling steps, and accelerates the training convergence considerably. On average, our training procedure improves the generation quality by 12% in FID compared to standard rectified flow and 7% compared to previous baselines under a fixed sampling budget. Code available at: https://github.com/NazirNayal8/MixFlow

Nazir Nayal, Christopher Wewer, Jan Eric Lenssen

Max Planck Institute for Informatics, Saarland Informatics Campus, Germany

Rectified FlowImage GenerationFlow-Based Generative ModelingFew-Step Diffusion Sampling
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Apr 10, 2026

Discrete Meanflow Training Curriculum

Flow-based image generative models exhibit stable training and produce high quality samples when using multi-step sampling procedures. One-step generative models can produce high quality image samples but can be difficult to optimize as they often exhibit unstable training dynamics. Meanflow models exhibit excellent few-step sampling performance and tantalizing one-step sampling performance. Notably, MeanFlow models that achieve this have required extremely large training budgets. We significantly decrease the amount of computation and data budget it takes to train Meanflow models by noting and exploiting a particular discretization of the Meanflow objective that yields a consistency property which we formulate into a ``Discrete Meanflow'' (DMF) Training Curriculum. Initialized with a pretrained Flow Model, DMF curriculum reaches one-step FID 3.36 on CIFAR-10 in only 2000 epochs. We anticipate that faster training curriculums of Meanflow models, specifically those fine-tuned from existing Flow Models, drives efficient training methods of future one-step examples.

Chia-Hong Hsu, Frank Wood

Department of Computer Science, University of British Columbia, Vancouver, BC, Canada

Flow-Based Generative ModelingMeanFlowOne-Step Generative Modeling
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Apr 9, 2026

Equivariant Efficient Joint Discrete and Continuous MeanFlow for Molecular Graph Generation

Graph-structured data jointly contain discrete topology and continuous geometry, which poses fundamental challenges for generative modeling due to heterogeneous distributions, incompatible noise dynamics, and the need for equivariant inductive biases. Existing flow-matching approaches for graph generation typically decouple structure from geometry, lack synchronized cross-domain dynamics, and rely on iterative sampling, often resulting in physically inconsistent molecular conformations and slow sampling. To address these limitations, we propose Equivariant MeanFlow (EQUIMF), a unified SE(3)-equivariant generative framework that jointly models discrete and continuous components through synchronized MeanFlow dynamics. EQUIMF introduces a unified time bridge and average-velocity updates with mutual conditioning between structure and geometry, enabling efficient few-step generation while preserving physical consistency. Moreover, we develop a novel discrete MeanFlow formulation with a simple yet effective parameterization to support efficient generation over discrete graph structures. Extensive experiments demonstrate that EQUIMF consistently outperforms prior diffusion and flow-matching methods in generation quality, physical validity, and sampling efficiency.

Rongjian Xu, Teng Pang, Zhiqiang Dong +1

School of Software, Shandong University, Jinan, Shandong, China · School of Software, Shandong University, Jinan, Shandong, China; Luke EI, Jinan, China

Molecular Graph GenerationGenerative Modeling3D Molecular GenerationFlow-Based Generative ModelingFlow MatchingDiscrete Flow Matching
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Apr 7, 2026

Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space

High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as diffusion models and Flow Matching, have shown promising performance, they are fundamentally constrained by their discrete, pixel-based nature. This limitation restricts their applicability in turbulence computing, where data inherently exists in a functional form. To address this gap, we propose Functional Optimal Transport Conditional Flow Matching (FOT-CFM), a generative framework defined directly in infinite-dimensional function space. Unlike conventional approaches defined on fixed grids, FOT-CFM treats physical fields as elements of an infinite-dimensional Hilbert space, and learns resolution-invariant generative dynamics directly at the level of probability measures. By integrating Optimal Transport (OT) theory, we construct deterministic, straight-line probability paths between noise and data measures in Hilbert space. This formulation enables simulation-free training and significantly accelerates the sampling process. We rigorously evaluate the proposed system on a diverse suite of chaotic dynamical systems, including the Navier-Stokes equations, Kolmogorov Flow, and Hasegawa-Wakatani equations, all of which exhibit rich multi-scale turbulent structures. Experimental results demonstrate that FOT-CFM achieves superior fidelity in reproducing high-order turbulent statistics and energy spectra compared to state-of-the-art baselines.

Li Kunpeng, Wan Chenguang, Qu Zhisong +5

Flow-Based Generative ModelingFlow MatchingComputational Fluid DynamicsOptimal Transport
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