Flow-Based Generative Modeling

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

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Latest papers 331

May 13, 2026cs.LG

Support-Conditioned Flow Matching Is Kernel Smoothing

Generative models are often conditioned on a small set of examples via cross-attention. Under the Gaussian optimal-transport path, we show that the exact velocity field induced by a finite support set is a Nadaraya--Watson kernel smoother whose bandwidth decreases with flow time, from broad averaging at early steps to nearest-neighbor at late steps. A single Gaussian-kernel attention head exactly computes this field, connecting cross-attention conditioning to classical kernel theory. The theory predicts three failure regimes: nearest-neighbor collapse of the kernel at high dimension, mismatch between the isotropic kernel and the data geometry, and insufficient support for nonparametric estimation. Experiments on Gaussian mixtures, spherical shells, and DINOv2 ImageNet features confirm that learned conditioning improves in precisely these regimes, and that IP-Adapter's cross-attention implements approximate NW smoothing in practice.

Daniel Matsui Smola

Department of Computer Science University of Washington Seattle, WA

Flow Matching Cross-Attention Kernel Methods Flow-Based Generative Modeling Conditional Generative Modeling

May 13, 2026cs.CV

Asymmetric Flow Models

Flow-based generation in high-dimensional spaces is difficult because velocity prediction requires modeling high-dimensional noise, even when data has strong low-rank structure. We present Asymmetric Flow Modeling (AsymFlow), a rank-asymmetric velocity parameterization that restricts noise prediction to a low-rank subspace while keeping data prediction full-dimensional. From this asymmetric prediction, AsymFlow analytically recovers the full-dimensional velocity without changing the network architecture or training/sampling procedures. On ImageNet 256

\times

256, AsymFlow achieves a leading 1.57 FID, outperforming prior DiT/JiT-like pixel diffusion models by a large margin. AsymFlow also provides the first-ever route for finetuning pretrained latent flow models into pixel-space models: aligning the low-rank pixel subspace to the latent space gives a seamless initialization that preserves the latent model's high-level semantics and structure, so finetuning mainly improves low-level mismatches rather than relearning pixel generation. We show that the pixel AsymFlow model finetuned from FLUX.2 klein 9B establishes a new state of the art for pixel-space text-to-image generation, beating its latent base on HPSv3, DPG-Bench, and GenEval while qualitatively showing substantially improved visual realism.

Hansheng Chen, Jan Ackermann, Minseo Kim +2

Stanford University

Flow Matching T2I Generation Image Generation Pixel-Space Diffusion Models Generative Modeling Flow-Based Generative Modeling

May 13, 2026stat.ML

Coreset-Induced Conditional Velocity Flow Matching

We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution. Hierarchical flow matching models the full conditional velocity law in velocity space, but its inner flow is asked to transport isotropic Gaussian noise to a multimodal target velocity distribution from scratch. Our key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target. CCVFM first compresses the target into weighted atoms using an entropic Sinkhorn coreset and lifts them to a Gaussian mixture. The induced conditional velocity law is then a closed-form Gaussian mixture that can be sampled without a learned neural sampler. A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual rather than learning an entire noise-to-data map. We prove that the surrogate transport cost equals the target--surrogate Wasserstein gap under an explicit compression assumption, whereas the noise-source analogue has a dimension-scale lower bound. We further characterize the conditional second moment of the direct surrogate-source training target and show that its source-dependent excess is small when the surrogate conditional law is close to the true conditional velocity law in mean and covariance. Empirically, on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ, the proposed method reaches competitive few-step generation under matched architectures.

Xiao Wang, Zihua She, Jianxi Su

Department of Statistics, Purdue University

Conditional Flow Matching Rectified Flow Flow-Based Generative Modeling Conditional Generative Modeling

May 12, 2026cs.LG

Discrete MeanFlow: One-Step Generation via Conditional Transition Kernels

MeanFlow enables one-step generation in continuous spaces by learning an average velocity over a time interval rather than the instantaneous velocity field of flow matching. However, discrete state spaces do not have smooth trajectories or spatial derivatives, so the continuous formulation does not directly apply. We introduce Discrete MeanFlow, which replaces the motion of a point with the transport of probability mass over finite states. Our key object is the conditional transition kernel of a continuous-time Markov chain (CTMC), from which we define a mean discrete rate that measures the average change in transition probability over a time interval. We prove a Discrete MeanFlow identity that relates this finite-interval rate to the instantaneous CTMC generator at the endpoint, with the Kolmogorov forward equation replacing the spatial chain rule of continuous MeanFlow. Based on this identity, we parameterize the transition kernel directly using a boundary-by-construction design that guarantees valid probability outputs and exact boundary conditions without auxiliary losses. Since the learned kernel is itself a probability distribution, generation reduces to a single forward pass followed by one categorical draw meaning no iterative denoising, ODE integration, or multi-step refinement is required. We validate the framework on exact finite-state Markov chains, where the learned kernel recovers the analytical ground truth to high precision, and on factorized synthetic sequence generation tasks with varying alphabet sizes and sequence lengths.

Fairoz Nower Khan, Nabuat Zaman Nahim, Md Sajid Ahmed +2

Department of Computer Science, University of Kentucky Lexington, Kentucky 40506, USA

Markov Models MeanFlow One-Step Generative Modeling Generative Modeling Mean Flow Flow-Based Generative Modeling+1

May 12, 2026cs.LG

Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling

Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the integration of physics-based constraints into the generation process, existing approaches fail to enforce strict constraint satisfaction while maintaining sample quality. In particular, training-free constrained sampling methods, while providing per-sample feasibility guarantees, introduce a fundamental mismatch between the training objective and the constrained sampling procedure, often leading to performance degradation. Identifying this training-sampling misalignment as a central limitation of current constrained generative modeling approaches, this paper proposes Constraint-Aware Flow Matching, a novel end-to-end framework that explicitly incorporates constraint projections into the training objective. By aligning the model's learned dynamics with the constrained sampling process, the proposed method mitigates distributional shift induced by projection-based corrections, enabling high-quality constrained generation. The proposed approach is evaluated on three challenging real-world benchmarks, illustrating the generality and efficacy of the method.

Jacob K. Christopher, James E. Warner, Ferdinando Fioretto

University of Virginia · NASA Langley Research Center

Constrained Generative Modeling Flow Matching Generative Modeling Flow-Based Generative Modeling

May 12, 2026cs.LG

Aligning Flow Map Policies with Optimal Q-Guidance

Generative policies based on expressive model classes, such as diffusion and flow matching, are well-suited to complex control problems with highly multimodal action distributions. Their expressivity, however, comes at a significant inference cost: generating each action typically requires simulating many steps of the generative process, compounding latency across sequential decision-making rollouts. We introduce flow map policies, a novel class of generative policies designed for fast action generation by learning to take arbitrary-size jumps including one-step jumps-across the generative dynamics of existing flow-based policies. We instantiate flow map policies for offline-to-online reinforcement learning (RL) and formulate online adaptation as a trust-region optimization problem that improves the critic's Q-value while remaining close to the offline policy. We theoretically derive FLOW MAP Q-GUIDANCE (FMQ), a principled closed-form learning target that is optimal for adapting offline flow map policies under a critic-guided trust-region constraint. We further introduce Q-GUIDED BEAM SEARCH (QGBS), a stochastic flow-map sampler that combines renoising with beam search to enable iterative inference-time refinement. Across 12 challenging robotic manipulation and locomotion tasks from OGBench and RoboMimic, FMQ achieves state-of-the-art performance in offline-to-online RL, outperforming the previous one-step policy MVP by a relative improvement of 21.3% on the average success rate.

Christos Ziakas, Alessandra Russo, Avishek Joey Bose

Imperial College London · Mila

Flow Matching Policy Optimization Flow-Based Generative Modeling RL for Generative Models Inference-Time Guidance Offline-To-Online RL

May 12, 2026cs.CV

$h$ -control: Training-Free Camera Control via Block-Conditional Gibbs Refinement

Training-free camera control for pretrained flow-matching video generators is a partial-observation inverse problem: a depth-warped guidance video supplies noisy evidence on a subset of latent sites, which the sampler must reconcile with the pretrained prior. Existing methods struggle to balance the trade-off between trajectory adherence and visual quality and the heuristic guidance-strength tuning lacks robustness. We propose \textbf{

h

-control}, which resolves this dilemma through a structural change to the sampler: each outer hard-replacement guidance step is augmented with an inner-loop \emph{block-conditional pseudo-Gibbs refinement} on the unobserved complement at the same noise level, with provable convergence to the partial-observation conditional data law. To accelerate convergence on high-dimensional video latents, we exploit their conditional locality, partitioning the unobserved complement into 3D patches, each tracked by a custom mixing indicator that adaptively freezes converged patches. On RealEstate10K and DAVIS, \textbf{

h

-control} attains the best FVD against all seven training-free and training-based competitors, outperforming every training-free baseline on every reported metric.

Yuzhu Wang, Xi Ye, Duo Su +2

Department of Computer Science and Technology, Tsinghua University · South China University of Technology

Markov Chain Monte Carlo Camera-Controlled Video Generation Diffusion Guidance Flow-Based Generative Modeling Controllable Video Generation

May 12, 2026cs.LG

One-Step Generative Modeling via Wasserstein Gradient Flows

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a generator that transforms samples from a simple reference distribution into samples from a target data distribution in a single step. This is achieved in two steps: we first define an evolution from the reference distribution to the target distribution through a Wasserstein gradient flow that minimizes an energy functional; second, we train a static neural generator to compress this evolution into one-step generation. We instantiate the energy functional with the Sinkhorn divergence, which yields an efficient optimal-transport-based update rule that captures global distributional discrepancy and improves coverage of the target distribution. We further prove that the finite-sample training dynamics converge to the continuous-time distributional dynamics under suitable assumptions. Empirically, W-Flow sets a new state of the art for one-step ImageNet 256

\times

256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100

\times

faster sampling. These results show that Wasserstein gradient flows provide a principled and effective foundation for fast and high-fidelity generative modeling.

Jiaqi Han, Puheng Li, Qiushan Guo +3

Stanford University · ByteDance

Wasserstein Gradient Flows Image Generation One-Step Generative Modeling Generative Modeling Flow-Based Generative Modeling

May 12, 2026cs.LG

Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching

Flow matching models generate samples by numerically integrating a learned velocity field, with each integration step requiring a neural network evaluation. Fast generation therefore requires using a small fixed evaluation budget effectively: the key question is not only how to integrate the flow, but where the sampler should spend its steps. We propose SharpEuler, a training-free sampler that profiles a pretrained model offline by estimating where the learned velocity field changes most rapidly along calibration trajectories. This finite-difference estimate defines a solver-aware sharpness profile, which is smoothed and converted by a quantile transform into a timestep grid for any desired inference budget. At test time, sampling remains ordinary Euler integration with the same number of model evaluations as a uniform schedule. We justify SharpEuler using three principles: a numerical principle identifying trajectory acceleration as the leading source of Euler discretization error, a variational principle deriving sharpness-based power-law timestep densities, and a statistical guarantee showing that the finite-sample calibrated sampler is stable at the terminal distribution level. Our experiments show that SharpEuler improves sample quality at fixed budgets, reducing inter-mode leakage and increasing mode coverage.

Aditi Gupta, Soon Hoe Lim, Annan Yu +1

Lawrence Berkeley National Laboratory · International Computer Science Institute · 1Lawrence Berkeley National Laboratory, 2International Computer Science Institute +4

Flow Matching Flow-Based Generative Modeling

May 11, 2026cs.LG

Language Modeling with Hyperspherical Flows

Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. Recent Flow Language Models (FLMs) apply continuous flows to language, transporting noise to data with a deterministic ODE that avoids factorized sampling. FLMs operate on one-hot vectors whose dimension scales with the vocabulary size, making FLMs costly to train. Moreover, since all distinct one-hot embeddings are equidistant in

\ell_2

, adding Gaussian noise does not have a clear semantic interpretation (unlike images, where Gaussian noise progressively degrades structure). We introduce

\mathbb{S}

-FLM, a latent FLM in the hypersphere.

\mathbb{S}

-FLM generates sequences by rotating vectors in

\mathbb{S}^{d-1}

along a velocity field learned with cross-entropy, avoiding the overhead of materializing one-hot vectors. Previous FLMs match AR in Generative Perplexity (Gen.\ PPL), but samples with high likelihood are not necessarily correct in verifiable domains such as math and code.

\mathbb{S}

-FLM substantially improves continuous flow language models on large-vocabulary reasoning and closes the gap to masked diffusion under standard-temperature sampling (

T=1

), while a gap remains under optimized low-temperature (

T=0.1

) decoding.

Justin Deschenaux, Caglar Gulcehre

EPFL · Lausanne, Switzerland · EPFL, Lausanne, Switzerland +1

Normalizing Flows Continuous Normalizing Flows Language Modeling Flow-Based Generative Modeling

May 11, 2026cs.CL

ELF: Embedded Language Flows

Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their image-domain counterparts, today's leading diffusion language models (DLMs) primarily operate over discrete tokens. In this paper, we show that continuous DLMs can be made effective with minimal adaptation to the discrete domain. We propose Embedded Language Flows (ELF), a class of diffusion models in continuous embedding space based on continuous-time Flow Matching. Unlike existing DLMs, ELF predominantly stays within the continuous embedding space until the final time step, where it maps to discrete tokens using a shared-weight network. This formulation makes it straightforward to adapt established techniques from image-domain diffusion models, e.g., classifier-free guidance (CFG). Experiments show that ELF substantially outperforms leading discrete and continuous DLMs, achieving better generation quality with fewer sampling steps. These results suggest that ELF offers a promising path toward effective continuous DLMs.

Keya Hu, Linlu Qiu, Yiyang Lu +5

MIT

Flow-Based Generative Modeling Diffusion Language Models Continuous Diffusion Language Models

May 11, 2026cs.LG

Follow the Mean: Reference-Guided Flow Matching

Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.

Pedro M. P. Curvo, Maksim Zhdanov, Floor Eijkelboom +1

University of Amsterdam · AMLab

Flow Matching Flow-Based Generative Modeling Conditional Generative Modeling Controllable Image Generation

May 11, 2026cs.LG

UFO: A Unified Flow-Oriented Framework for Robust Continual Graph Learning

Graph learning research has increasingly shifted toward continual graph learning (CGL), which better reflects real-world scenarios where graphs evolve over time. However, existing CGL methods largely assume clean supervision and overlook a critical challenge: the newly arriving portions of the graph are often noisy, due to annotation errors or adversarial corruption. This mismatch limits their applicability in practice. In this work, we study robust continual graph learning, where models must simultaneously handle catastrophic forgetting and noisy supervision in evolving graph data. We show that label noise introduces a new failure mode, catastrophic remembering, where models persistently reinforce corrupted knowledge across tasks. To address these challenges, we propose a Unified Flow-Oriented framework (UFO). First, UFO models conditional feature distributions via flow-based generative modeling and produces replay representations, mitigating forgetting without storing historical data. Second, UFO estimates instance-level reliability scores to distinguish clean from noisy nodes, reducing the impact of corrupted supervision and alleviating catastrophic remembering. Extensive experiments on four benchmark graph datasets under varying noise ratios demonstrate that UFO consistently outperforms existing methods in both accuracy and forgetting metrics. Code is available at: https://anonymous.4open.science/r/UFO.

Danhui Zhang, Zhe Wang, Qing Qing +6

Jilin University · Adelaide University · RMIT University +1

Replay-Based Continual Learning Flow-Based Generative Modeling Learning with Noisy Labels

May 10, 2026cs.CV

Offline Preference Optimization for Rectified Flow with Noise-Tracked Pairs

Existing preference datasets for text-to-image models typically store only the final winner/loser images. This representation is insufficient for rectified flow (RF) models, whose generation is naturally indexed by a specific prior noise sample and follows a nearly straight denoising trajectory. In contrast, prior DPO-style alignment for diffusion models commonly estimates trajectories using an independent forward noising process, which can be mismatched to the true reverse dynamics and introduces unnecessary variance. We propose Prior Noise-Aware Preference Optimization (PNAPO), an off-policy alignment framework specialized for rectified flow. PNAPO augments preference data by retaining the paired prior noises used to generate each winner/loser image, turning the standard (prompt, winner, loser) triplet into a sextuple. Leveraging the straight-line property of RF, we estimate intermediate states via noise-image interpolation, which constrains the trajectory estimation space and yields a tighter surrogate objective for preference optimization. In addition, we introduce a dynamic regularization strategy that adapts the DPO regularization based on (i) the reward gap between winner and loser and (ii) training progress, improving stability and sample efficiency. Experiments on state-of-the-art RF T2I backbones show that PNAPO consistently improves preference metrics while substantially reducing training compute.

Yunhong Lu, Qichao Wang, Hengyuan Cao +2

Zhejiang University · Shanghai Institute for Advanced Study-Zhejiang University · Shanghai Institute for Mathematics and Interdisciplinary Sciences

Pairwise Preference Learning Rectified Flow Text-Image Alignment T2I Generation Flow-Based Generative Modeling Offline Preference Optimization

May 10, 2026eess.AS

Kinetic-Optimal Scheduling with Moment Correction for Metric-Induced Discrete Flow Matching in Zero-Shot Text-to-Speech

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject

Dong Yang, Yiyi Cai, Haoyu Zhang +2

1The University of Tokyo · 2Independent Researcher

Flow Matching TTS Synthesis Zero-Shot TTS Flow-Based Generative Modeling Discrete Flow Matching

May 10, 2026cs.LG

dFlowGRPO: Rate-Aware Policy Optimization for Discrete Flow Models

Discrete flow models (DFMs) are a class of flexible generative models for generating discrete data, and diffusion large language models (dLLMs) can be viewed as a special case with a specific choice of a mixture path and a masked source distribution. While several recent works have explored reinforcement learning for dLLMs, its application to more general discrete flow models remains underexplored. In this work, we present discrete Flow-GRPO (dFlowGRPO), a unified reinforcement learning framework for discrete flow models that supports a broad family of probability paths and non-masked source distributions. We derive the full trajectory probability for DFMs and formulate the denoising process as a Markov decision process, enabling dFlowGRPO to incorporate information from both the associated conditional transition rates and the posterior model during reinforcement learning. We apply dFlowGRPO to FUDOKI, a recent multimodal discrete flow model, and evaluate it on both image generation and multimodal understanding tasks. Empirical results show that dFlowGRPO outperforms existing GRPO-type methods for dLLMs on text-to-image generation tasks and achieves performance competitive with continuous flow-based models trained using Flow-GRPO, while also demonstrating strong capabilities on understanding tasks.

Zhengyan Wan, Yidong Ouyang, Panwen Hu +1

Mohamed bin Zayed University of Artificial Intelligence · East China Normal University · University of California, Los Angeles +1

Group Relative Policy Optimization Image Generation Flow-Based Generative Modeling RL for Generative Models Multimodal Understanding

May 10, 2026cs.LG

On Variance Reduction in Learning Mean Flows

One-step generative modeling has emerged as a leading approach for amortizing the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and unbounded gradient variance. In this work, we establish a theory that attributes this pathology to a misuse of the conditional velocity field. We show that the conditional velocity plays two distinct statistical roles in the loss: both as an unbiased regression target and as a Monte Carlo control variate in a Jacobi-vector product, with the original MeanFlow loss assigning the wrong coefficient to the latter. We derive the optimal coefficient in closed form and show that a family of fixes in concurrent works corresponds to different practical realizations of the same optimum. A controlled sweep of this coefficient on two-dimensional benchmarks and on a latent Diffusion Transformer recovers the predicted bias-variance ordering. Our DiT experiment also reveals a quantitative FID-MSE landscape mismatch. Specifically, although the gradient-MSE is minimized at an interior coefficient value near

β\!=\!0.94

, the coefficient that minimizes FID prefers to use conditional velocity directly at the unbiased corner. Our analysis therefore explains why MeanFlow is unstable and unifies its concurrent remedies, and shows that the variance-optimal coefficient need not coincide with the quality-optimal one.

Juanwu Lu, Ziran Wang

Purdue University

Flow Matching MeanFlow One-Step Generative Modeling Mean Flow Flow-Based Generative Modeling Variance Reduction

May 9, 2026cs.LG

Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution

μ_1

from samples drawn from a source distribution

μ_0

. This framework relies on a fixed coupling between

μ_0

and

μ_1

, and on a deterministic or stochastic bridge to define an interpolating process between the two distributions. The time marginals of this process can then be approximately sampled by estimating the transition rates, or more generally the generator, of its Markovian projection. This framework has recently been extended to the case of discrete source and target distributions, under the name Discrete Flow Matching (DFM). However, theoretical guarantees for such models remain scarce. In this paper, we study two DFM models on

\mathbb{Z}_m^d = \{0,\ldots,m-1\}^d

, sampled through time discretization, and derive non-asymptotic associated bounds for both of them. In contrast to previous work, we establish non-asymptotic bounds in Kullback--Leibler divergence for the early-stopped version of the target distribution. We also derive explicit convergence guarantees in total variation distance with respect to the true target distribution. Importantly, these bounds rely only on an approximation error assumption, relaxing standard score assumptions used in earlier works, while also yielding improved dependence on the vocabulary size

m

and the dimension

d

.

Le-Tuyet-Nhi Pham, Giovanni Conforti, Zhenjie Ren +1

École Polytechnique, CMAP, IP Paris Route de Saclay, 91120 Palaiseau, France · Università degli Studi di Padova, Via Trieste, 63, 35131 Padova, Italia · LaMME, Université Évry Paris-Saclay Boulevard François Mitterrand 91000, France

Flow Matching Generative Modeling Flow-Based Generative Modeling Discrete Flow Matching

May 9, 2026cs.CV

Restoration-Aligned Generative Flow Models for Blind Motion Deblurring

Generative flow models offer powerful priors learned from large-scale natural images, but directly adapting them to restoration tasks such as motion deblurring causes severe fidelity degradation, as their training objective is inherently misaligned with restoration. We present DeblurFlow, a framework that resolves this misalignment by reformulating the flow trajectory itself: we replace the noise endpoint with the blur observation, which makes the underlying vector field coincide with the residual error between blur and clean images. Under this formulation, the standard flow matching loss naturally takes the form of a residual loss, allowing pretrained flow models to be optimized under restoration-aligned objectives via LoRA adaptation. This formulation further enables a dual-expert sampling strategy: a fidelity expert provides a high-fidelity initialization, e.g., PSNR 33.69 dB, and DeblurFlow enhances perceptual quality with only a marginal fidelity reduction to 33.05 dB, whereas directly applying a generative model on top of a fidelity expert decreases PSNR to 27.60 dB. To make this practical, we further introduce r-space, a latent space tailored for residual decoding rather than image reconstruction, which reduces encoder-decoder cost by up to 9

\times

over standard VAE latents. Extensive experiments on GoPro, HIDE, RealBlur, and RWBI demonstrate that DeblurFlow achieves strong restoration fidelity and perceptual realism, while remaining computationally practical.

Insoo Kim, Jinwoo Shin

1NAVER Cloud · 2KAIST AI

Flow Matching Image Deblurring Generative Flow Networks Image Restoration Flow-Based Generative Modeling

May 9, 2026cs.LG

Deterministic Decomposition of Stochastic Generative Dynamics

Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic generative models capture richer density evolution through drift and diffusion. Yet when stochastic dynamics are described through deterministic velocity fields, the effects of drift and diffusion are often compressed into a single effective field, obscuring the distinct roles of deterministic evolution and stochastic fluctuation. In this work, we show that the deterministic field

b_t

of a stochastic generative process admits a natural transport--osmotic decomposition that separates deterministic transport from stochastic, diffusion-induced effects:

b_t = u_t + d_t

, where

u_t

governs marginal probability transport and

d_t

captures an osmotic effect induced by diffusion and determined by the marginal score. Based on this decomposition, we propose Bridge Matching, a flow-based framework for learning decomposed generative dynamics through both marginal and conditional formulations. In generative modeling experiments, we recombine the learned components as

b_t = u_t + λ_d d_t

, showing that the proposed decomposition enables interpretable and controllable sampling by adjusting the osmotic contribution in probability transport.

Xingyu Song, Yuan Mei, Naoya Takeishi

1The University of Tokyo · 2Zhejiang University · *Visiting student at The University of Tokyo from Zhejiang University.

Flow Matching Stochastic Differential Equations Generative Modeling Flow-Based Generative Modeling

May 8, 2026cs.LG

Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once

Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability measures over probability measures, introducing a Wasserstein-on-Wasserstein (WoW) formulation. Leveraging the nested Wasserstein geometry, we show that measures over transport plans naturally induce velocity fields that realize metameasure flows. This yields a principled generalization of Wasserstein flow matching via coupled outer and inner transport plans. To address the substantial computational cost of WoW transport, we propose scalable approximations based on sliced and linear Wasserstein distances, enabling efficient training while promoting numerically stable, near-straight trajectories. Our framework unifies and extends existing approaches to point cloud and set generation, providing a practical and theoretically grounded method for generative modelling in WoW spaces.

Moritz Piening, Richard Duong, Gabriele Steidl

Institut für Mathematik, Technische Universität Berlin, Germany

Flow Matching Generative Modeling Point Cloud Generation Flow-Based Generative Modeling Optimal Transport

May 8, 2026cs.LG

Exploring and Exploiting Stability in Latent Flow Matching

In this work, we show that Latent Flow-Matching (LFM) models are robust to different types of perturbations, including data reduction and model capacity shrinkage. We characterize this stability by these models' tendency to generate similar outputs under identical noise seeds. We provide a perspective relating this phenomenon to flow matching theory, which indicates that this stability is inherent to the FM objective. We further exploit this stability to derive practical algorithms for more efficient training and inference. Concretely, first, we show that by training LFM models on significantly reduced datasets, performance is preserved, and in compute-constrained regimes, the model converges faster while maintaining quality. This yields multiple advantages, including savings in the training time due to faster convergence, and alleviating annotation effort when training conditional models. Second, LFM stability under architectural shrinkage gives rise to a two-model coarse-to-fine approach, one using a light-weight architecture for the first phase of the FM trajectory, and one with higher capacity for the second, thereby reducing the inference cost substantially. To determine which samples are informative, we introduce three sample-scoring criteria and evaluate them under standard metrics for generative models. Our results are thoroughly evaluated on multiple datasets, demonstrating the practical advantage of this stability, including data savings and a more than two-fold inference speedup while generating comparable outputs.

Rania Briq, Michael Kamp, Ohad Fried +2

Forschungszentrum Jülich · Technical University Dortmund · Lamarr Institute +4

Flow Matching Efficient Inference Generative Modeling Flow-Based Generative Modeling

May 8, 2026cs.LG

What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching

Recent work has shown that models flow matching models can be trained without explicit time conditioning, challenging the standard view that the interpolation time is needed to disambiguate velocity targets. But why should a time-blind model work at all? Decomposing the time-blind flow matching loss, we identify two sources of irreducible error: a coupling variance, which arises from ambiguous velocity targets induced by how noise and data points are paired, and the time-blindness gap, which is the additional error caused by ignoring time. This gap shows that time-blind training is strictly harder than conventional training, reinforcing the puzzle that time-blind models work so well in practice. We resolve this tension by showing that the geometry of high-dimensional data makes time identifiable directly from noisy observations. When data concentrates near a

k

-dimensional subspace, time can be recovered from the statistical structure of noisy interpolants in directions orthogonal to the data; under a spiked-covariance model, this yields a closed-form estimator that recovers

t

from a single observation

z

at rate

O(1/\sqrt{d-k})

for ambient dimension

d

. As a consequence, we prove that the time-blindness gap is asymptotically negligible relative to the coupling variance. We empirically demonstrate our identifiability result on real-world data and show that changing the coupling has a much larger effect on loss and sample quality than removing time conditioning across CIFAR-10, CelebA-HQ, and FFHQ. These results explain why time-blind flow matching works and show that the main practical lever is the choice of coupling, not explicit time conditioning.

Alec Helbling, Sebastian Gutierrez Hernandez, Benjamin Hoover +2

Georgia Tech · IBM Research

Flow Matching Flow-Based Generative Modeling

May 8, 2026cs.CV

Normalizing Trajectory Models

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

Jiatao Gu, Tianrong Chen, Ying Shen +3

Apple · UIUC

Normalizing Flows Diffusion Model Distillation Few-Step Diffusion Sampling Diffusion-Based Image Generation Flow-Based Generative Modeling Diffusion Models

May 8, 2026cs.CV

Flow-OPD: On-Policy Distillation for Flow Matching Models

Existing Flow Matching (FM) text-to-image models suffer from two critical bottlenecks under multi-task alignment: the reward sparsity induced by scalar-valued rewards, and the gradient interference arising from jointly optimizing heterogeneous objectives, which together give rise to a 'seesaw effect' of competing metrics and pervasive reward hacking. Inspired by the success of On-Policy Distillation (OPD) in the large language model community, we propose Flow-OPD, the first unified post-training framework that integrates on-policy distillation into Flow Matching models. Flow-OPD adopts a two-stage alignment strategy: it first cultivates domain-specialized teacher models via single-reward GRPO fine-tuning, allowing each expert to reach its performance ceiling in isolation; it then establishes a robust initial policy through a Flow-based Cold-Start scheme and seamlessly consolidates heterogeneous expertise into a single student via a three-step orchestration of on-policy sampling, task-routing labeling, and dense trajectory-level supervision. We further introduce Manifold Anchor Regularization (MAR), which leverages a task-agnostic teacher to provide full-data supervision that anchors generation to a high-quality manifold, effectively mitigating the aesthetic degradation commonly observed in purely RL-driven alignment. Built upon Stable Diffusion 3.5 Medium, Flow-OPD raises the GenEval score from 63 to 92 and the OCR accuracy from 59 to 94, yielding an overall improvement of roughly 10 points over vanilla GRPO, while preserving image fidelity and human-preference alignment and exhibiting an emergent 'teacher-surpassing' effect. These results establish Flow-OPD as a scalable alignment paradigm for building generalist text-to-image models. The codes and weights will be released in: https://github.com/CostaliyA/Flow-OPD .

Zhen Fang, Wenxuan Huang, Yu Zeng +8

University of Science and Technology of China · University of California, Los Angeles · 3The Chinese University of Hong Kong +1

Diffusion Model Alignment Flow Matching RL for Image Generation Flow-Based Generative Modeling On-Policy Distillation T2I Diffusion Models

May 8, 2026cs.CV

STARFlow2: Bridging Language Models and Normalizing Flows for Unified Multimodal Generation

Deep generative models have advanced rapidly across text and vision, motivating unified multimodal systems that can understand, reason over, and generate interleaved text-image sequences. Most existing approaches combine autoregressive language modeling with diffusion-based image generators, inheriting a structural mismatch between causal text generation and iterative visual denoising. We observe that autoregressive normalizing flows are autoregressive Transformers--sharing the same causal mask, KV-cache mechanism, and left-to-right structure as LLMs--making them the most natural paradigm for true unified multimodal generation. We present STARFlow2, built on the Pretzel architecture that vertically interleaves a pretrained VLM stream with a TarFlow stream via residual skip connections, both operating under the same causal mask. Combined with a deep-shallow flow design and a unified FAE latent space, STARFlow2 enables cache-friendly interleaved generation where both text and visual outputs directly enter the KV-cache without re-encoding. Experiments demonstrate strong performance across image generation and multimodal understanding benchmarks, validating autoregressive flows as a viable foundation for unified multimodal modeling.

Ying Shen, Tianrong Chen, Yuan Gao +6

UIUC · Apple

Unified Multimodal Models Multimodal Generation Autoregressive Image Generation Flow-Based Generative Modeling Multimodal Foundation Models

May 8, 2026cs.LG

Trajectory as the Teacher: Few-Step Discrete Flow Matching via Energy-Navigated Distillation

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Amin Karimi Monsefi, Dominic Culver, Nikhil Bhendawade +3

1The Ohio State University · 2Apple

Flow Matching Diffusion Language Model Inference Language Model Distillation Flow-Based Generative Modeling Teacher-Student Learning Discrete Flow Matching

May 8, 2026stat.ML

Consistency Regularised Gradient Flows for Inverse Problems

Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations (NFEs) and backpropagation through large pretrained components, leading to substantial computational costs and, in some cases, degraded reconstruction quality. We propose a unified Euclidean-Wasserstein-2 gradient-flow framework that jointly performs posterior sampling and prompt optimization in the latent space through a single flow that aligns the prior and posterior with the observed data. Combined with few-step latent text-to-image models, this formulation enables low-NFE inference without backpropagation through autoencoders. Experiments across several canonical imaging inverse problems show that our method achieves state-of-the-art performance with significantly reduced computational cost.

Alessio Spagnoletti, Tim Y. J. Wang, Marcelo Pereyra +1

Laboratoire MAP5, UMR 8145, Université Paris Cité, CNRS · Department of Mathematics, Imperial College London · Heriot-Watt University, MACS & Maxwell Institute

Latent Diffusion Models Wasserstein Gradient Flows Diffusion-Based Inverse Problems Flow-Based Generative Modeling Diffusion Posterior Sampling Image Inverse Problems

May 8, 2026cs.LG

Scaling Categorical Flow Maps

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including accelerated sampling and tilting. Recently, several works have demonstrated the possibility of generating discrete data continuously by a simple flow matching process between a Gaussian and the one-hot encoded data distribution. They have further shown the feasibility of accelerated sampling via Categorical Flow Maps (CFMs), resulting in competitive sample quality in the few-step regime. However, this method had only been evaluated at relatively modest scales (

<1

B), leaving the question of its scalability completely open. In this article, we train a

1.7

B-parameter base flow model on

2.1

T tokens and self-distill it into a CFM that generates diverse, high-quality text in as few as

4

inference steps while maintaining near-data-level token entropy. Furthermore, we introduce a likelihood bound for CFMs in the semi-discrete setting, and show that they can be used to score the model on standard LM benchmarks, achieving results in the same range as discrete diffusion methods. Finally, we uncover some of the challenges that arise from training these models at scale, and we provide prescriptive insights on loss weighting and time scheduling.

Oscar Davis, Anastasiia Filippova, Pierre Ablin +4

Apple · University of Oxford

Language Model Scaling Flow Map Learning Flow-Based Generative Modeling Continuous Diffusion Language Models Text Generation Discrete Flow Matching

May 8, 2026stat.ML

Flow Matching for Count Data

High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mappings between distributions across successive batches or time points form critical components of data analysis. The recent success of diffusion- and flow-based deep generative models for images, video, and text motivates extending these ideas to count-valued settings, but many existing methods either treat each count as a categorical state or transform counts into a continuous space, neither of which is natural or efficient when the count range is large. We propose count-FM, a flow-matching framework for count data based on a continuous-time birth-death process with local unit jumps. Count-FM learns marginal transitions efficiently in count space through simulation-free training of conditional transition rates, allowing transport between arbitrary count-distributed source and target populations. In simulation, count-FM variants achieve strong sample quality while using substantially fewer parameters. We further apply count-FM to scRNA-seq and neural spike-train data for unconditional generation, transport, and conditional generation. Across these tasks, count-FM yields improved sample quality, greater modeling efficiency, and interpretable transport paths.

Ganchao Wei, John Pearson

Department of Neurobiology Department of Statistical Science Duke University Durham, NC, USA · Department of Neurobiology Department of Electrical and Computer Engineering Duke University Durham, NC, USA

Flow Matching Synthetic Data Generation Flow-Based Generative Modeling

May 8, 2026cs.LG

Structured Coupling for Flow Matching

Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice generative quality. We bridge this gap by proposing Structured Coupling for Flow Matching (SCFM), a cooperative framework that augments flow matching with structured latent representation learning. By introducing structured latent variables and exogenous noise into the source, SCFM jointly learns a structured prior (via latent variable modeling) and a continuous transport map (via flow matching). It uses a shared time-dependent recognition network for both latent variable model variational inference and intermediate-time flow velocity estimation. This yields a structurally informed yet unconditional, simulation-free flow model, where the latent variable model can also assist flow sampling. Empirically, SCFM facilitates unsupervised latent representation learning for clustering, disentanglement and downstream tasks, while remaining competitive with flow matching in sample quality, showing that meaningful structure can be learned without sacrificing generative fidelity.

Xavier Sumba, Carles Balsells-Rodas, Yingzhen Li

Imperial College London

Flow Matching Disentangled Representation Learning Latent Variable Models Unsupervised Representation Learning Generative Modeling Flow-Based Generative Modeling

May 8, 2026cs.LG

Flow-Direct: Feedback-Efficient and Reusable Guidance for Flow Models via Non-Parametric Guidance Field

Training-free guidance enables pre-trained diffusion and flow models to optimize application-specific objectives using feedback from external black-box reward functions. However, existing methods are feedback-inefficient because reward feedback is used only transiently to inform a localized gradient approximation or a discrete search decision, and is subsequently discarded. To address this limitation, we propose Flow-Direct, a framework that guides the generation process via a persistent guidance field. Theoretically, this guidance field is analytically derived from the log-density ratio between the base and reward-weighted target distributions; it transports the pre-trained distribution to the target distribution. In practice, the field is implemented as a non-parametric estimator constructed from all accumulated reward-evaluated samples. As more samples are collected during optimization, this empirical guidance field becomes increasingly accurate. This persistent formulation yields two major advantages. First, Flow-Direct is highly feedback-efficient: because every evaluated sample is used to refine the global guidance field, no reward information is wasted. Second, the framework is naturally reusable: once optimization is complete, the collected dataset defines a reusable guidance field for generating novel target samples without additional reward evaluations, and distinct guidance fields can be combined to generate samples that simultaneously satisfy multiple objectives.

Kim Yong Tan, Yueming Lyu, Ivor Tsang +1

College of Computing and Data Science, Nanyang Technological University, Singapore · Centre for Frontier AI Research, Agency for Science, Technology and Research, Singapore · Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore

Diffusion Model Guidance Black-Box Optimization Flow-Based Generative Modeling Inference-Time Guidance

May 7, 2026cs.LG

Conservative Flows: A New Paradigm of Generative Models

Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized from data-supported states rather than from noise. The framework can utilize any pretrained flow model. We develop two probability-preserving sampling mechanisms, a corrected Langevin dynamics with a Metropolis adjustment and a predictor-corrector flow, that operate directly on existing checkpoints. We validate the framework on a synthetic Swiss-roll target, ImageNet-256 and Oxford Flowers-102, where our samplers consistently improve over the original generation procedures.

Eshed Gal, Md Shahriar Rahim Siddiqui, Moshe Eliasof +1

The University of British Columbia Vancouver, Canada · University of Cambridge Cambridge, United Kingdom

Langevin Dynamics Generative Flow Networks Generative Modeling Flow-Based Generative Modeling

May 7, 2026cs.LG

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

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

(ρ_t)_{t \in [0,1]}

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

Aditya Ranganath, Mukesh Singhal

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

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

May 7, 2026cs.AI

Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline

We propose a deterministic adjoint matching framework that formulates human preference alignment for flow-based generative models as an optimal control problem over velocity fields. One can directly regress the control toward a value-gradient-induced target under the current policy, leading to a simple and stable training objective. Building on this perspective, we introduce a truncated adjoint scheme that focuses computation on the terminal portion of the trajectory, where reward-relevant signals concentrate, which yields substantial computational savings while preserving alignment quality. We further generalize the framework beyond standard KL-based regularization, allowing more flexible trade-offs between alignment strength and distributional preservation. Experiments on SiT-XL/2 and FLUX.2-Klein-4B demonstrate consistent gains across multiple alignment metrics, along with substantially improved diversity and mode preservation.

Zhengyi Guo, Jiayuan Sheng, David D. Yao +1

Fine-Tuning Flow-Based Generative Modeling

May 7, 2026cs.CV

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

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

256\times256

and 2.38 FID at

512\times512

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

Mingfeng Lin, Jiakun Chen, Liang Han +1

Harbin Institute of Technology (Shenzhen)

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

May 7, 2026cs.LG

Flow Matching with Arbitrary Auxiliary Paths

We introduce a new generative modeling framework, \textbf{Flow Matching with Arbitrary Auxiliary Paths (AuxPath-FM)}, which generalizes conditional flow matching by incorporating an auxiliary variable drawn from an arbitrary distribution into the probability path. Unlike prior methods that restrict auxiliary components to Gaussian noise, AuxPath-FM allows the variable

η

to follow any distribution, producing trajectories of the form

X_t = a(t)X_1 + b(t)X_0 + c(t)η

. We theoretically demonstrate that this construction preserves the continuity equation and maintains a training objective consistent with the marginal formulation. This flexibility enables the design of diverse probability paths using various priors, including Gaussian, Uniform, Laplace, and discrete Rademacher distributions, each offering unique geometric properties for generative flows. Furthermore, our framework allows for specialized tasks such as label-guided generation by encoding structured semantic information into the auxiliary distribution. Overall, AuxPath-FM provides a principled and general foundation for probability path design, offering both theoretical generality and practical flexibility for diverse generative modeling tasks.

Xin Peng, Ang Gao

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

Conditional Flow Matching Flow-Based Generative Modeling Conditional Generative Modeling

May 7, 2026cs.LG

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

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

Tyler Ingebrand, Ruihan Zhao, Kushagra Gupta +3

University of Texas at Austin

Flow Matching Flow-Based Generative Modeling Conditional Generative Modeling

May 7, 2026cs.AI

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

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

Xin Peng, Ang Gao

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

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

May 7, 2026cs.LG

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

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

256 \times 256

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

12\times

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

23.1\%

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

Sicheng Ma, Tianyue Yang, Xiuzhe Wu +1

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

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

May 7, 2026cs.AI

SDFlow: Similarity-Driven Flow Matching for Time Series Generation

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

\textbf{S}

imilarity-

\textbf{D}

riven

\textbf{Flow}

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

Wei Li, Shibo Feng, Pengcheng Wu +3

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

Flow Matching Time Series Generation Flow-Based Generative Modeling

May 7, 2026stat.ML

Spherical Flows for Sampling Categorical Data

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

\mathbb S^{d-1}

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

\mathbb S^{d-1}

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

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

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

Jannis Chemseddine, Gregor Kornhardt, Gabriele Steidl

Technische Universität Berlin

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

May 6, 2026cs.RO

HDFlow: Hierarchical Diffusion-Flow Planning for Long-horizon Tasks

Recent advances in generative models have shown promise in generating behavior plans for long-horizon, sparse reward tasks. While these approaches have achieved promising results, they often lack a principled framework for hierarchical decomposition and struggle with the computational demands of real-time execution, due to their iterative denoising process. In this work, we introduce Hierarchical Diffusion-Flow (HDFlow), a novel hierarchical planning framework that optimally leverages the strengths of diffusion and rectified flow models to overcome the limitations of single-paradigm generative planners. HDFlow employs a high-level diffusion planner to generate sequences of strategic subgoals in a learned latent space, capitalizing on diffusion's powerful exploratory capabilities. These subgoals then guide a low-level rectified flow planner that generates smooth and dense trajectories, exploiting the speed and efficiency of ordinary differential equation (ODE)-based trajectory generation. We evaluate HDFlow on four challenging furniture assembly tasks in both simulation and real-world, where it significantly outperforms state-of-the-art methods. Furthermore, we also showcase our method's generalizability on two long-horizon benchmarks comprising diverse locomotion and manipulation tasks. Project website: https://hdflow-page.github.io/

Nandiraju Gireesh, Yuanliang Ju, Chaoyi Xu +3

1Peking University · University of Toronto. · 2Galbot

Hierarchical Planning Long-Horizon Robotic Manipulation Trajectory Generation Diffusion-Based Planning Robot Motion Generation Flow-Based Generative Modeling

May 5, 2026cs.LG

A Few-Step Generative Model on Cumulative Flow Maps

We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and \revise{cumulative} parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction \revise{instantiation}. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

Zhiqi Li, Duowen Chen, Yuchen Sun +1

Georgia Institute of Technology, Atlanta, United States of America

One-Step Generative Modeling Flow-Based Generative Modeling Diffusion Model Acceleration

May 5, 2026cs.LG

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.

Hao Zhou, Rui Zhang, Han Wan +1

Gaoling School of Artificial Intelligence, Renmin University of China

Physics-Informed Generative Modeling Uncertainty Quantification Rectified Flow Generative Modeling Physics-Informed ML Flow-Based Generative Modeling+1

May 4, 2026cs.GR

Generative Modeling with Orbit-Space Particle Flow Matching

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

Sinan Wang, Jinjin He, Shenyifan Lu +3

Georgia Institute of Technology, USA

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

May 3, 2026cs.LG

Stable GFlowNets with Probabilistic Guarantees

Generative Flow Networks (GFlowNets) learn to sample states proportional to an unnormalized reward. Despite their theoretical promise, practical training is often unstable, exhibiting severe loss spikes and mode collapse. To tackle this, we first assess the sensitivity of GFlowNet objectives, demonstrating that a small Total Variation (TV) distance between the learned and target distributions does not preclude unbounded training loss. Motivated by this mismatch, we establish converse guarantees by deriving loss-to-TV bounds that certify global fidelity from bounded trajectory balance losses. Lastly, we propose Stable GFlowNets, an algorithm that leverages our theoretical results to stabilize training, and empirically demonstrate improved training behavior and superior distributional fidelity.

Zengxiang Lei, Ananth Shreekumar, Jonathan Rosenthal +6

Lyles School of Civil and Construction Engineering, Purdue University, IN, USA · Department of Computer Science, Purdue University, IN, USA · Computer Science and Engineering, University of California, Santa Cruz, USA

Generative Flow Networks Flow-Based Generative Modeling

May 2, 2026cs.AI

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

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

Guowei Zou, Haitao Wang, Beiwen Zhang +2

Sun Yat-sen University

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

May 1, 2026cs.CV

Posterior Augmented Flow Matching

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

George Stoica, Sayak Paul, Matthew Wallingford +6

Georgia Tech · University of Washington · Hugging Face +2

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

May 1, 2026cs.LG

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

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

10^4 \times

less total compute than ensembling or Monte Carlo dropout.

Jiarui Xing, Song Wang, Jian Wang

Yale University · Harvard Medical School

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

May 1, 2026cs.LG

Binomial flows: Denoising and flow matching for discrete ordinal data

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

Yair Shenfeld, Ricardo Baptista, Stefano Peluchetti

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

Apr 30, 2026stat.ML

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 Control Diffusion Sampling Diffusion Model Fine-Tuning Flow-Based Generative Modeling Score-Based Generative Modeling

Apr 29, 2026cs.LG

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 \textit{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 \textit{deterministic optimal control problem}, yielding a hierarchy of algorithms that subsumes existing approaches at the coarsest level. We show that the \textit{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 \textbf{Flow Map Reward Guidance (FMRG)}: a training-free, \textit{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 \textbf{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 Modeling Flow-Based Generative Modeling Conditional Generative Modeling

Apr 28, 2026cs.RO

FlowS: One-Step Motion Prediction via Local Transport Conditioning

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

K

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

Leandro Di Bella, Adrian Munteanu, Bruno Cornelis

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

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

Apr 27, 2026cs.LG

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 Modeling Continuous Normalizing Flows Flow-Based Generative Modeling Matrix Completion

Apr 26, 2026cs.AR

FlowPlace: Flow Matching for Chip Placement

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

\times

faster sampling efficiency, and zero overlaps.

Peng Xie, Ke Xue, Yunqi Shi +6

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

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

Apr 25, 2026cs.CV

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 \textit{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 Matching Text-to-Motion Generation Human Motion Generation Flow-Based Generative Modeling

Apr 21, 2026cs.CV

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 Flows Autoregressive Image Generation Flow-Based Generative Modeling

Apr 21, 2026cs.LG

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 Matching Image Generation Flow-Based Generative Modeling

Apr 19, 2026cs.LG

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

Zero-Shot Time Series Forecasting Healthcare Synthetic Data Generation Continuous Normalizing Flows Prior-Data Fitted Networks Flow-Based Generative Modeling+1