Flow-Based Generative Modeling

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

Jul 13Week of Sep 28

Latest papers 331

May 31, 2026cs.LG

Strong Stochastic Flow Maps

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

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

University of Bath · 2AITHYRA

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

May 29, 2026cs.LG

Geometric Erasure by Contrastive Velocity Matching in Rectified Flows

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

Jonas Henry Grebe, Tobias Braun, Anna Rohrbach +1

Technical University of Darmstadt & hessian.AI, Germany.

Rectified Flow Flow-Based Generative Modeling Concept Erasure

May 28, 2026cs.LG

Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design

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

Sven Gutjahr, Riccardo De Santi, Luca Schaufelberger +2

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

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

May 28, 2026cs.LG

Midpoint Generative Models

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

t=1/2

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

Daniil Shlenskii, Nikita Gushchin, Lev Novitskiy +2

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

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

May 27, 2026cs.LG

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

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

Julien Lalanne, David Picard, Lionel Boillot +3

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

Flow Matching Uncertainty Quantification Generative Modeling Flow-Based Generative Modeling

May 27, 2026cs.LG

Parameter-Efficient Generative Modeling with Controlled Vector Fields

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

Peyman Morteza

Generative Modeling Continuous Normalizing Flows Flow-Based Generative Modeling

May 26, 2026cs.LG

GenSBI: Generative Methods for Simulation-Based Inference in JAX

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

Aurelio Amerio

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

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

May 26, 2026cs.LG

Recursive Flow Matching

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

\times

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

Jiahe Huang, Sihan Xu, Sharvaree Vadgama +1

University of California, San Diego · University of Michigan

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

May 25, 2026cs.LG

Two-Parameter Flows for Learning Population Dynamics of Physical Systems

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

Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer

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

Dynamical Systems Continuous Normalizing Flows Flow-Based Generative Modeling

May 25, 2026cs.LG

AdvantageFlow: Regularized Advantage-Weighted RL in Flow Models

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

Branislav Kveton, Anup Rao, Subhojyoti Mukherjee +2

Adobe Research

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

May 22, 2026cs.CV

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

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

8\times

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

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

Eindhoven University of Technology, Eindhoven

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

May 22, 2026cs.RO

Sparse Compositional Flow Matching by geometric assembly from motion primitives

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

Yan Tang, Yuanbo Tang, Tingyu Cao +2

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

Flow Matching Robot Motion Generation Flow-Based Generative Modeling

May 22, 2026cs.LG

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

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

\ell_2

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

Junru Zhang, Lang Feng, Jinbo Wang +6

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

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

May 20, 2026cs.AI

Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards

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

g^\text{car}

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

g^\text{car}

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

g^\text{car}

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

Xuehui Yu, Fucheng Cai, Meiyi Wang +2

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

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

May 19, 2026cs.CV

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

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

\rightarrow

image, image

\rightarrow

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

\rightarrow

image FID from

62.7

to

31.6

and image

\rightarrow

text CIDEr from

2.0

to

99.4

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

{\sim}84

,GB to

{\sim}38

,GB and raising throughput by

{\sim}8\times

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

{\sim}5\%

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

Eric Tillmann Bill, Enis Simsar, Alessio Tonioni +1

ETH Zurich · Google

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

May 19, 2026cs.CV

Probability-Conserving Flow Guidance

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

Parsa Esmati, Junha Hyung, Amirhossein Dadashzadeh +2

University of Bristol · KAIST

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

May 19, 2026stat.ML

Tail Annealing for Heavy-Tailed Flow Matching

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

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

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

d

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

W_1

, CVaR

_{99}

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

Jean Pachebat

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

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

May 19, 2026cs.CV

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

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

Yi Sun, Zhiqi Zhang, Xinhao Zhong +5

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

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

May 19, 2026cs.CV

Multi-Scale Generative Modeling with Heat Dissipation Flow Matching

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

x

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

x

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

Jun Ma, Hanquan Zhang, Yanjun Qin +2

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

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

May 19, 2026cs.GR

Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes

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

Tianshu Kuai, Arman Maesumi, Daniel Ritchie +1

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

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

May 19, 2026cs.CV

Distribution Matching Distillation without Fake Score Network

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

256 \times 256

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

Youngjoong Kim, Deokyeong Lee, Jaesik Park

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

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

May 18, 2026stat.ML

Flowing with Confidence

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

k

ensembles or stochastic trajectories at

k\times

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

Friso de Kruiff, Dario Coscia, Max Welling +1

CuspAI · AMLab, University of Amsterdam · mathLab, SISSA

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

May 18, 2026cs.CV

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

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

256 \times 256

and

512 \times 512

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

Longtao Jiang, Jianmin Bao, Zhendong Wang +4

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

Normalizing Flows Embedding Compression Flow-Based Generative Modeling

May 17, 2026astro-ph.IM

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

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

Tianyue Yang, Sandro Tacchella, Xiao Xue

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

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

May 17, 2026cs.LG

Drift Flow Matching

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

Chenrui Ma, Xi Xiao, Lin Zhao +3

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

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

May 16, 2026cs.LG

Learning Unbiased Permutations via Flow Matching

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

Yimeng Min, Carla P. Gomes

Department of Computer Science Cornell University Ithaca, NY, USA

Flow Matching Combinatorial Optimization Flow-Based Generative Modeling

May 16, 2026cs.CV

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

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

Anuska Roy, Pravin Nair

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

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

May 15, 2026cs.LG

Wavelet Flow Matching for Multi-Scale Physics Emulation

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

Gabriele Accarino, Juan Nathaniel, Carla Roesch +4

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

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

May 15, 2026stat.ML

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

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

\mathcal{O}(D^2)

to compute exactly or

\mathcal{O}(D)

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

Gurjeet Jagwani, Stephen Thorp, Sinan Deger +1

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

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

May 15, 2026cs.LG

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

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

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

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

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