Flow-Based Generative Modeling

Follow this topic Ask about this topic

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

Latest papers

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

Mar 6, 2026

RAC: Rectified Flow Auto Coder

In this paper, we propose a Rectified Flow Auto Coder (RAC) inspired by Rectified Flow to replace the traditional VAE: 1. It achieves multi-step decoding by applying the decoder to flow timesteps. Its decoding path is straight and correctable, enabling step-by-step refinement. 2. The model inherently supports bidirectional inference, where the decoder serves as the encoder through time reversal (hence Coder rather than encoder or decoder), reducing parameter count by nearly 41%. 3. This generative decoding method improves generation quality since the model can correct latent variables along the path, partially addressing the reconstruction--generation gap. Experiments show that RAC achieves a Pareto improvement over SOTA VAEs, where even a 10

\times

parameter-reduced decoder exceeds full-scale VAE performance in both reconstruction and generation quality, validating the effectiveness of our approach.

Sen Fang, Yalin Feng, Yanxin Zhang +6

Autoencoders Variational Autoencoders Flow-Based Generative Modeling

Mar 5, 2026

RelaxFlow: Text-Driven Amodal 3D Generation

Image-to-3D generation faces inherent semantic ambiguity under occlusion, where partial observation alone is often insufficient to determine object category. In this work, we formalize text-driven amodal 3D generation, where text prompts steer the completion of unseen regions while strictly preserving input observation. Crucially, we identify that these objectives demand distinct control granularities: rigid control for the observation versus relaxed structural control for the prompt. To this end, we propose RelaxFlow, a training-free dual-branch framework that decouples control granularity via a Multi-Prior Consensus Module and a Relaxation Mechanism. Theoretically, we prove that our relaxation is equivalent to applying a low-pass filter on the generative vector field, which suppresses high-frequency instance details to isolate geometric structure that accommodates the observation. To facilitate evaluation, we introduce two diagnostic benchmarks, ExtremeOcc-3D and AmbiSem-3D. Extensive experiments demonstrate that RelaxFlow successfully steers the generation of unseen regions to match the prompt intent without compromising visual fidelity.

Jiayin Zhu, Guoji Fu, Xiaolu Liu +3

National University of Singapore · Zhejiang University · University of Science and Technology of China

Text-to-3D Generation 3D Shape Completion Flow-Based Generative Modeling

Mar 4, 2026

Linearized Coupling Flow with Shortcut Constraints for One-Step Face Restoration

Face restoration can be formulated as a continuous-time transformation between image distributions via Flow Matching (FM). However, standard FM typically employs independent coupling, ignoring the statistical correlation between low-quality (LQ) and high-quality (HQ) data. This leads to intersecting trajectories and high velocity-field curvature, requiring multi-step integration. We propose Shortcut-constrained Coupling Flow for Face Restoration (SCFlowFR) to address these challenges. By establishing a data-dependent coupling, we explicitly model the LQ-HQ dependency to minimize path crossovers and promote near-linear probability flow. Furthermore, we employ a conditional mean estimator to refine the source distribution's anchor, effectively tightening the transport cost and stabilizing the velocity field. To ensure stable one-step inference, a shortcut constraint is introduced to supervise average velocities over arbitrary intervals, mitigating discretization bias in large-step updates. SCFlowFR achieves state-of-the-art one-step restoration, providing a superior trade-off between perceptual fidelity and computational efficiency.

Xiaohui Sun, Hanlin Wu

School of Information Science and Technology, Beijing Foreign Studies University, Beijing 100089, China

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

Mar 2, 2026

Preconditioned Flow Matching

Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions

p_t

. We identify a geometric optimization bottleneck in this regression problem: when the covariance

Σ_t

of

p_t

is ill-conditioned, gradient-based training rapidly fits high-variance directions while making slow progress along low-variance ones. In an exactly solvable Gaussian setting, we prove that the excess risk is weighted by

Σ_t

, and that both gradient descent and stochastic gradient descent inherit condition-number-dependent convergence. We then extend the analysis to Gaussian mixtures, showing that multimodality does not average away this effect; instead, the slowest and worst-conditioned component can control optimization. Motivated by this analysis, we propose

\textit{preconditioned flow matching}

, a precondition-then-match framework that transforms the target distribution into a more isotropic representation, trains the main flow in the transformed space, and maps generated samples back through the inverse transformation. We show theoretically that preconditioning reshapes the intermediate FM path and improves its conditioning. Across controlled Gaussian and Gaussian-mixture experiments, latent MNIST and other high resolution image datasets up to

512{\times}512

resolution, preconditioning improves path-conditioning diagnostics, low-eigenvalue recovery, FID, MMD, precision, and recall. Compute-matched baselines and preconditioner-quality ablations further show that the gains are not explained merely by additional preconditioner parameters, but by improved geometry of the downstream flow matching problem. GitHub: https://github.com/ahxmeds/preconditioned-flow-matching.git.

Shadab Ahamed, Eshed Gal, Md Shahriar Rahim Siddiqui +3

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

Flow Matching Flow-Based Generative Modeling

Mar 1, 2026

AG-REPA: Causal Layer Selection for Representation Alignment in Audio Flow Matching

REPresentation Alignment (REPA) improves the training of generative flow models by aligning intermediate hidden states with pretrained teacher features, but its effectiveness in token-conditioned audio Flow Matching critically depends on the choice of supervised layers, which is typically made heuristically based on the depth. In this work, we introduce Attribution-Guided REPresentation Alignment (AG-REPA), a novel causal layer selection strategy for representation alignment in audio Flow Matching. Firstly, we find that layers that best store semantic/acoustic information (high teacher-space similarity) are not necessarily the layers that contribute most to the velocity field that drives generation, and we call it Store-Contribute Dissociation (SCD). To turn this insight into an actionable training guidance, we propose a forward-only gate ablation (FoG-A) that quantifies each layer's causal contribution via the induced change in the predicted velocity field, enabling sparse layer selection and adaptive weighting for alignment. Across unified speech and general-audio training (LibriSpeech + AudioSet) under different token-conditioning topologies, AG-REPA consistently outperforms REPA baselines. Overall, our results show that alignment is most effective when applied to the causally dominant layers that drive the velocity field, rather than to layers that are representationally rich but functionally passive.

Pengfei Zhang, Tianxin Xie, Minghao Yang +1

AI Thrust, Information Hub, The Hong Kong University of Science and Technology (Guangzhou).

Flow-Based Generative Modeling Flow Matching Audio Representation Learning Feature Attribution

Mar 1, 2026

Active Flow Matching

Discrete diffusion and flow matching models capture complex, non-additive and non-autoregressive structure in high-dimensional objective landscapes through parallel, iterative refinement. However, their implicit generative nature precludes direct integration with principled variational frameworks for online black-box optimisation, such as variational search distributions (VSD) and conditioning by adaptive sampling (CbAS). We introduce Active Flow Matching (AFM), which reformulates variational objectives to operate on conditional endpoint distributions along the flow, enabling gradient-based steering of flow models toward high-fitness regions while preserving the rigour of VSD and CbAS. We derive forward and reverse Kullback-Leibler (KL) variants using self-normalised importance sampling. Across a suite of online protein and small molecule design tasks, forward-KL AFM consistently performs competitively compared to state-of-the-art baselines, demonstrating effective exploration-exploitation under tight experimental budgets.

Yashvir S. Grewal, Daniel M. Steinberg, Thang D. Bui +2

School of Computing, College of Systems and Society, Australian National University, Australia · Data61, CSIRO, Australia

Molecule Design Flow-Based Generative Modeling Black-Box Optimization Variational Inference

Feb 28, 2026

Generalizing Score-based generative models for Heavy-tailed Distributions

Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although dedicated models for heavy-tailed distributions have been proposed, their generative fidelity remains unclear and they lack solid theoretical foundations, leaving important questions open in this regime. In this paper, we address this gap through two theoretical contributions. First, we show that combining early stopping with a suitable initialization is sufficient to extend the diffusion framework to any target distribution; in particular, we establish the well-posedness of the backward process and prove convergence of the approximated diffusion in KL divergence. Second, we derive novel theoretical guarantees for generation with normalizing flows, obtaining convergence results that hold under mild conditions on the flow family and without any assumption on the tail behavior of the target distribution. Building on these results, we propose a unified generative framework for heavy-tailed distributions: a normalizing flow is first trained to capture the tail behavior and is then used as an initialization prior for an SGM, which refines the samples by recovering fine-grained structural details. This design leverages the complementary strengths of the two model classes within a theoretically principled pipeline, overcoming the limitations of existing approaches.

Tiziano Fassina, Gabriel Cardoso, Sylvan Le Corff +1

STIM, Mines Paris Paris, France · LPSM, Sorbonne Université Paris, France

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

Feb 27, 2026

Flowette: Flow Matching with Graphette Priors for Graph Generation

We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework that employs a graph neural network-based transformer to learn a velocity field over graph representations with node and edge attributes. Our model promotes topology-aware alignment through optimal transport-based coupling and preserves structural fidelity through endpoint- and chemistry-aware regularisation. To incorporate domain-driven structural priors, we introduce graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs such as rings, stars, and trees. We theoretically analyze the coupling, invariance, and structural properties of the framework, evaluate it on synthetic and molecular benchmarks, and isolate the contributions of the structural prior, the optimal-transport coupling, and the regularisation terms through controlled ablations. Flowette achieves competitive performance overall, attaining state-of-the-art results on several metrics across multiple benchmarks, highlighting the effectiveness of combining structural priors with flow-based training for modeling complex graph distributions.

Asiri Wijesinghe, Sevvandi Kandanaarachchi, Daniel M. Steinberg +1

CSIRO’s Data61 · Australian National University

Graph Generation Flow-Based Generative Modeling Molecular Graph Generation

Feb 26, 2026

ProjFlow: Projection Sampling with Flow Matching for Zero-Shot Exact Spatial Motion Control

Generating human motion with precise spatial control is a challenging problem. Existing approaches often require task-specific training or slow optimization, and enforcing hard constraints frequently disrupts motion naturalness. Building on the observation that many animation tasks can be formulated as a linear inverse problem, we introduce ProjFlow, a training-free sampler that achieves zero-shot, exact satisfaction of linear spatial constraints while preserving motion realism. Our key advance is a novel kinematics-aware metric that encodes skeletal topology. This metric allows the sampler to enforce hard constraints by distributing corrections coherently across the entire skeleton, avoiding the unnatural artifacts of naive projection. Furthermore, for sparse inputs, such as filling in long gaps between a few keyframes, we introduce a time-varying formulation using pseudo-observations that fade during sampling. Extensive experiments on representative applications, motion inpainting, and 2D-to-3D lifting, demonstrate that ProjFlow achieves exact constraint satisfaction and matches or improves realism over zero-shot baselines, while remaining competitive with training-based controllers.

Akihisa Watanabe, Qing Yu, Edgar Simo-Serra +1

Waseda University · LY Corporation

Human Motion Generation Flow-Based Generative Modeling

Feb 25, 2026

Flow Matching is Adaptive to Manifold Structures

Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source distribution (e.g., a standard normal) and a target data distribution. Flow-based methods often exhibit greater training stability and have achieved strong empirical performance in high-dimensional settings where data concentrate near a low-dimensional manifold, such as text-to-image synthesis, video generation, and molecular structure generation. Despite this success, existing theoretical analyses of flow matching assume target distributions with smooth, full-dimensional densities, leaving its effectiveness in manifold-supported settings largely unexplained. To this end, we theoretically analyze flow matching with linear interpolation when the target distribution is supported on a smooth manifold. We establish a non-asymptotic convergence guarantee for the learned velocity field, and then propagate this estimation error through the ODE to obtain statistical consistency of the implicit density estimator induced by the flow-matching objective. The resulting convergence rate is near minimax-optimal, depends only on the intrinsic dimension, and reflects the smoothness of both the manifold and the target distribution. Together, these results provide a principled explanation for how flow matching adapts to intrinsic data geometry and circumvents the curse of dimensionality.

Shivam Kumar, Yixin Wang, Lizhen Lin

Booth School of Business, University of Chicago · Department of Statistics, University of Michigan · Department of Mathematics, University of Maryland, College Park

Flow Matching Generative Modeling Flow-Based Generative Modeling Statistical Learning Theory

Feb 25, 2026

Entropy-Controlled Flow Matching

Modern vision generators transport a base distribution to data through time-indexed measures, implemented as deterministic flows (ODEs) or stochastic diffusions (SDEs). Despite strong empirical performance, standard flow-matching objectives do not directly control the information geometry of the trajectory, allowing low-entropy bottlenecks that can transiently deplete semantic modes. We propose Entropy-Controlled Flow Matching (ECFM): a constrained variational principle over continuity-equation paths enforcing a global entropy-rate budget d/dt H(mu_t) >= -lambda. ECFM is a convex optimization in Wasserstein space with a KKT/Pontryagin system, and admits a stochastic-control representation equivalent to a Schrodinger bridge with an explicit entropy multiplier. In the pure transport regime, ECFM recovers entropic OT geodesics and Gamma-converges to classical OT as lambda -> 0. We further obtain certificate-style mode-coverage and density-floor guarantees with Lipschitz stability, and construct near-optimal collapse counterexamples for unconstrained flow matching.

Chika Maduabuchi

William & Mary, Williamsburg, VA, USA

Flow Matching Flow-Based Generative Modeling Entropy Regularization Optimal Transport

Feb 24, 2026

Provably Safe Generative Sampling with Constricting Barrier Functions

Flow-based generative models, such as diffusion models and flow matching models, have achieved remarkable success in learning complex data distributions. However, a critical gap remains for their deployment in safety-critical domains: the lack of formal guarantees that generated samples will satisfy hard constraints. We propose a safety filtering framework that acts as an online shield for any pre-trained generative model. Our key insight is to cooperate with the generative process rather than override it. We define a constricting safety tube that is relaxed at the initial noise distribution and progressively tightens to the target safe set at the final data distribution, mirroring the coarse-to-fine structure of the generative process itself. By characterizing this tube via Control Barrier Functions (CBFs), we synthesize a feedback control input through a convex Quadratic Program (QP) at each sampling step. As the tube is loosest when noise is high and intervention is cheapest in terms of control energy, most constraint enforcement occurs when it least disrupts the model's learned structure. We prove that this mechanism guarantees safe sampling in discrete-time. The minimum-norm control synthesized at each step minimizes the per-step contribution to the KL divergence between the safe and original distributions. Across all experiments, we observe 100% constraint satisfaction. Our framework applies to any pre-trained flow-based sampling scheme requiring no retraining or architectural modifications. We validate the approach across constrained image generation, physically-consistent trajectory sampling, and safe robotic manipulation policies, achieving 100% constraint satisfaction while preserving semantic fidelity.

Darshan Gadginmath, Ahmed Allibhoy, Fabio Pasqualetti

Mitsubishi Electric Research Laboratories Cambridge, Massachusetts · Electrical Engineering and Computer Science University of California, Irvine

Constrained Sampling Constrained Generative Modeling Flow-Based Generative Modeling

Feb 24, 2026

A Long-Short Flow-Map Perspective for Drifting Models

This paper provides a reinterpretation of the Drifting Model~\cite{deng2026generative} through a semigroup-consistent long-short flow-map factorization. We show that a global transport process can be decomposed into a long-horizon flow map followed by a short-time terminal flow map admitting a closed-form optimal velocity representation, and that taking the terminal interval length to zero recovers exactly the drifting field together with a conservative impulse term required for flow-map consistency. Based on this perspective, we propose a new likelihood learning formulation that aligns the long-short flow-map decomposition with density evolution under transport. We validate the framework through both theoretical analysis and empirical evaluations on benchmark tests, and further provide a theoretical interpretation of the feature-space optimization while highlighting several open problems for future study.

Zhiqi Li, Bo Zhu

School of Interactive Computing, Georgia Institute of Technology

Drifting Models Flow Map Learning Generative Modeling Flow-Based Generative Modeling

Feb 23, 2026

Momentum Guidance: Plug-and-Play Guidance for Flow Models

Flow-based generative methods offer a simple and effective framework for high-fidelity generation, yet pretrained flow models are rarely used in their vanilla conditional form: in image generation, samples without guidance often appear diffuse and lack fine-grained detail. Existing guidance techniques such as classifier-free guidance (CFG) improve fidelity but reduce sample diversity. We introduce Momentum Guidance (MG), a guidance method that improves sample quality by extrapolating the current velocity away from an exponential moving average of past velocities along the ODE trajectory, while preserving the standard one-evaluation-per-step cost. MG provides gains beyond CFG, improving the precision-recall Pareto frontier. Experiments demonstrate the effectiveness of MG across benchmarks. On ImageNet-256, MG improves FID by 36.54% without CFG and 25.42% with CFG on average across sampling settings, attaining an FID of 1.553 at 16 sampling steps. Evaluations on large flow-based models, including Stable Diffusion 3 and FLUX.1-dev, further confirm improvements across standard metrics.

Runlong Liao, Jian Yu, Baiyu Su +3

The University of Texas at Austin, Austin, TX 78712, USA

Momentum Methods Diffusion Guidance Image Generation Generative Modeling Flow-Based Generative Modeling Inference-Time Guidance

Feb 23, 2026

MeanFuser: Fast One-Step Multi-Modal Trajectory Generation and Adaptive Reconstruction via MeanFlow for End-to-End Autonomous Driving

Generative models have shown great potential in trajectory planning. Recent studies demonstrate that anchor-guided generative models are effective in modeling the uncertainty of driving behaviors and improving overall performance. However, these methods rely on discrete anchor vocabularies that must sufficiently cover the trajectory distribution during testing to ensure robustness, inducing an inherent trade-off between vocabulary size and model performance. To overcome this limitation, we propose MeanFuser, an end-to-end autonomous driving method that enhances both efficiency and robustness through three key designs. (1) We introduce Gaussian Mixture Noise (GMN) to guide generative sampling, enabling a continuous representation of the trajectory space and eliminating the dependency on discrete anchor vocabularies. (2) We adapt ``MeanFlow Identity" to end-to-end planning, which models the mean velocity field between GMN and trajectory distribution instead of the instantaneous velocity field used in vanilla flow matching methods, effectively eliminating numerical errors from ODE solvers and significantly accelerating inference. (3) We design a lightweight Adaptive Reconstruction Module (ARM) that enables the model to implicitly select from all sampled proposals or reconstruct a new trajectory when none is satisfactory via attention weights.Experiments on the NAVSIM closed-loop benchmark demonstrate that MeanFuser achieves outstanding performance without the supervision of the PDM Score and exceptional inference efficiency, offering a robust and efficient solution for end-to-end autonomous driving. Our code and model are available at https://github.com/wjl2244/MeanFuser.

Junli Wang, Yinan Zheng, Xueyi Liu +9

SKL-MAIS, Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Xiaomi EV +1

Autonomous Driving Planning End-to-End Autonomous Driving Flow-Based Generative Modeling One-Step Generative Modeling Mean Flow

Feb 23, 2026

An LLM-Enabled Frequency-Aware Flow Diffusion Model for Natural-Language-Guided Power System Scenario Generation

Diverse and controllable scenario generation (e.g., wind, solar, load, etc.) is critical for robust power system planning and operation. As AI-based scenario generation methods are becoming the mainstream, existing methods (e.g., Conditional Generative Adversarial Nets) mainly rely on a fixed-length numerical conditioning vector to control the generation results, facing challenges in user conveniency and generation flexibility. In this paper, a natural-language-guided scenario generation framework, named LLM-enabled Frequency-aware Flow Diffusion (LFFD), is proposed to enable users to generate desired scenarios using plain human language. First, a pretrained LLM module is introduced to convert generation requests described by unstructured natural languages into ordered semantic space. Second, instead of using standard diffusion models, a flow diffusion model employing a rectified flow matching objective is introduced to achieve efficient and high-quality scenario generation, taking the LLM output as the model input. During the model training process, a frequency-aware multi-objective optimization algorithm is introduced to mitigate the frequency-bias issue. Meanwhile, a dual-agent framework is designed to create text-scenario training sample pairs as well as to standardize semantic evaluation. Experiments based on large-scale photovoltaic and load datasets demonstrate the effectiveness of the proposed method.

Zhenghao Zhou, Yiyan Li, Fei Xie +5

College of Smart Energy, Shanghai Non-Carbon Energy Conversion and Utilization Institute, and Key Laboratory of Control of Power Transmission and Conversion, Ministry of Education, Shanghai Jiao Tong University, Shanghai, 200240, China. · Qinghai Photovoltaic Industry Innovation Center Co., Ltd., State Power Investment Corporation, Xining 810007, China. · Xinjiang Hami Co., Ltd., State Power Investment Corporation, Hami 839000, China. +1

Conditional Generative Modeling Power Systems Flow-Based Generative Modeling

Feb 23, 2026

Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling

Crystal modeling spans a family of conditional and unconditional generation tasks, including crystal structure prediction (CSP) and de novo generation (DNG). While recent deep generative models have shown promising performance, they remain largely task-specific, lacking a unified framework that shares crystal representations across tasks. To address this limitation, we propose Multimodal Crystal Flow (MCFlow), a unified multimodal flow model that realizes multiple crystal generation tasks as distinct inference trajectories via independent time variables for atom types and crystal structures. To enable multimodal flow in a standard transformer model, we introduce a composition- and symmetry-aware atom ordering with hierarchical permutation augmentation, injecting compositional and crystallographic priors without explicit structural templates. Experiments on the MP-20 and MPTS-52 benchmarks show that a single MCFlow model is competitive with task-specific baselines across CSP, DNG, and structure-conditioned atom type generation.

Kiyoung Seong, Sungsoo Ahn, Sehui Han +1

Graduate School of AI, KAIST, Seoul, South Korea · Materials Intelligence Lab, LG AI Research, Seoul, South Korea

Crystal Structure Generation Unified Multimodal Models Crystal Structure Prediction Flow-Based Generative Modeling

Feb 23, 2026

Laplacian Multi-scale Flow Matching for Generative Modeling

In this paper, we present Laplacian multiscale flow matching (LapFlow), a novel framework that enhances flow matching by leveraging multi-scale representations for image generative modeling. Our approach decomposes images into Laplacian pyramid residuals and processes different scales in parallel through a mixture-of-transformers (MoT) architecture with causal attention mechanisms. Unlike previous cascaded approaches that require explicit renoising between scales, our model generates multi-scale representations in parallel, eliminating the need for bridging processes. The proposed multi-scale architecture not only improves generation quality but also accelerates the sampling process and promotes scaling flow matching methods. Through extensive experimentation on CelebA-HQ and ImageNet, we demonstrate that our method achieves superior sample quality with fewer GFLOPs and faster inference compared to single-scale and multi-scale flow matching baselines. The proposed model scales effectively to high-resolution generation (up to 1024

\times

1024) while maintaining lower computational overhead.

Zelin Zhao, Petr Molodyk, Haotian Xue +1

Georgia Institute of Technology Atlanta, GA 30332, USA

Mixture-of-Transformers Generative Modeling Flow-Based Generative Modeling Flow Matching

Feb 22, 2026

AdsorbFlow: energy-conditioned flow matching enables fast and realistic adsorbate placement

Identifying low-energy adsorption geometries on catalytic surfaces is a practical bottleneck for computational heterogeneous catalysis: the difficulty lies not only in the cost of density functional theory (DFT) but in proposing initial placements that relax into the correct energy basins. Conditional denoising diffusion has improved success rates, yet requires

\sim

100 iterative steps per sample. Here we introduce AdsorbFlow, a deterministic generative model that learns an energy-conditioned vector field on the rigid-body configuration space of adsorbate translation and rotation via conditional flow matching. Energy information enters through classifier-free guidance conditioning -- not energy-gradient guidance -- and sampling reduces to integrating an ODE in as few as 5 steps. On OC20-Dense with full DFT single-point verification, AdsorbFlow with an EquiformerV2 backbone achieves 61.4% SR@10 and 34.1% SR@1 -- surpassing AdsorbDiff (31.8% SR@1, 41.0% SR@10) at every evaluation level and AdsorbML (47.7% SR@10) -- while using 20 times fewer generative steps and achieving the lowest anomaly rate among generative methods (6.8%). On 50 out-of-distribution systems, AdsorbFlow retains 58.0% SR@10 with a MLFF-to-DFT gap of only 4~percentage points. These results establish that deterministic transport is both faster and more accurate than stochastic denoising for adsorbate placement.

Jiangjie Qiu, Wentao Li, Honghao Chen +2

Beijing Key Laboratory of Artificial Intelligence for Advanced Chemical Engineering Materials, Department of Chemical Engineering, Tsinghua University, Beijing, China.

Flow-Based Generative Modeling Materials Science Flow Matching

Feb 21, 2026

GenPlanner: From Noise to Plans -- Emergent Reasoning in Flow Matching and Diffusion Models

Path planning in complex environments is one of the key problems of artificial intelligence because it requires simultaneous understanding of the geometry of space and the global structure of the problem. In this paper, we explore the potential of using generative models as planning and reasoning mechanisms. We propose GenPlanner, an approach based on diffusion models and flow matching, along with two variants: DiffPlanner and FlowPlanner. We demonstrate the application of generative models to find and generate correct paths in mazes. A multi-channel condition describing the structure of the environment, including an obstacle map and information about the starting and destination points, is used to condition trajectory generation. Unlike standard methods, our models generate trajectories iteratively, starting with random noise and gradually transforming it into a correct solution. Experiments conducted show that the proposed approach significantly outperforms the baseline CNN model. In particular, FlowPlanner demonstrates high performance even with a limited number of generation steps.

Agnieszka Polowczyk, Alicja Polowczyk, Michał Wieczorek

Silesian University of Technology, Faculty of Applied Mathematics, Gliwice, 44-100, Poland

Diffusion-Based Planning Motion Planning Conditional Generative Modeling Flow-Based Generative Modeling

Feb 20, 2026

From Static Spectra to Operando Infrared Dynamics: Physics Informed Flow Modeling and a Benchmark

The Solid Electrolyte Interphase (SEI) is critical to the performance of lithium-ion batteries, yet its analysis via Operando Infrared (IR) spectroscopy remains experimentally complex and expensive, which limits its accessibility for standard research facilities. To overcome this bottleneck, we formulate a novel task, Operando IR Prediction, which aims to forecast the time-resolved evolution of spectral ``fingerprints'' from a single static spectrum. To facilitate this, we introduce OpIRSpec-7K, the first large-scale operando dataset comprising 7,118 high-quality samples across 10 distinct battery systems, alongside OpIRBench, a comprehensive evaluation benchmark with carefully designed protocols. Addressing the limitations of standard spectrum, video, and sequence models in capturing voltage-driven chemical dynamics and complex composition, we propose Aligned Bi-stream Chemical Constraint (ABCC), an end-to-end physics-aware framework. It reformulates MeanFlow and introduces a novel Chemical Flow to explicitly model reaction trajectories, employs a two-stream disentanglement mechanism for solvent-SEI separation, and enforces physics and spectrum constraints such as mass conservation and peak shifts. ABCC significantly outperforms state-of-the-art static, sequential, and generative baselines. ABCC even generalizes to unseen systems and enables interpretable downstream recovery of SEI formation pathways, supporting AI-driven electrochemical discovery.

Shuquan Ye, Ben Fei, Hongbin Xu +2

Department of Information Engineering, The Chinese University of Hong Kong · Shenzhen Loop Area Institute · Massachusetts Institute of Technology +1

Infrared Spectroscopy Physics-Informed Generative Modeling Flow-Based Generative Modeling Lithium-Ion Batteries

Feb 19, 2026

Conditional Flow Matching for Continuous Anomaly Detection in Autonomous Driving on a Manifold-Aware Spectral Space

Safety validation for Level 4 autonomous vehicles (AVs) is currently bottlenecked by the inability to scale the detection of rare, high-risk long-tail scenarios using traditional rule-based heuristics. We present Deep-Flow, an unsupervised framework for safety-critical anomaly detection that utilizes Optimal Transport Conditional Flow Matching (OT-CFM) to characterize the continuous probability density of expert human driving behavior. Unlike standard generative approaches that operate in unstable, high-dimensional coordinate spaces, Deep-Flow constrains the generative process to a low-rank spectral manifold via a Principal Component Analysis (PCA) bottleneck. This ensures kinematic smoothness by design and enables the computation of the exact Jacobian trace for numerically stable, deterministic log-likelihood estimation. To resolve multi-modal ambiguity at complex junctions, we utilize an Early Fusion Transformer encoder with lane-aware goal conditioning, featuring a direct skip-connection to the flow head to maintain intent-integrity throughout the network. We introduce a kinematic complexity weighting scheme that prioritizes high-energy maneuvers (quantified via path tortuosity and jerk) during the simulation-free training process. Evaluated on the Waymo Open Motion Dataset (WOMD), our framework achieves an AUC-ROC of 0.766 against a heuristic golden set of safety-critical events. More significantly, our analysis reveals a fundamental distinction between kinematic danger and semantic non-compliance. Deep-Flow identifies a critical predictability gap by surfacing out-of-distribution behaviors, such as lane-boundary violations and non-normative junction maneuvers, that traditional safety filters overlook. This work provides a mathematically rigorous foundation for defining statistical safety gates, enabling objective, data-driven validation for the safe deployment of autonomous fleets.

Antonio Guillen-Perez

Independent Researcher

Unsupervised Anomaly Detection Autonomous Driving Safety Evaluation Flow-Based Generative Modeling Conditional Flow Matching

Feb 18, 2026

Flow Map Language Models: One-step Language Modeling via Continuous Denoising

Language models based on discrete diffusion have attracted widespread interest for their potential to provide faster generation than autoregressive models. Despite their promise, these models typically produce samples whose quality sharply degrades in the few-step regime, preventing a dramatic speedup in practice. Here, we show that language models based on continuous flows over one-hot token embeddings can outperform discrete diffusion in both quality and speed. Importantly, our continuous formulation defines a unique flow map that can be learned directly for efficient few-step inference, a structure we show is unavailable to discrete methods. In this setting, we show that both the flow and its associated flow map can be learned with simple cross-entropy objectives that respect the simplex geometry of the data, and we identify three distinct choices for flow map distillation whose performance we compare in practice. Using these insights, we build a flow language model (FLM), a continuous flow that matches state-of-the-art discrete diffusion baselines on the One Billion Words (LM1B) and OpenWebText (OWT) datasets. We then distill FLM into a flow map language model (FMLM), whose one-step generation exceeds the 8-step quality of recent few-step discrete diffusion language models. Our work challenges the widely-held hypothesis that discrete noising processes are necessary for generative modeling over discrete modalities and paves the way toward accelerated language modeling at scale. Code is available at https://github.com/david3684/flm.

Chanhyuk Lee, Jaehoon Yoo, Manan Agarwal +6

KAIST · Carnegie Mellon University

Continuous Diffusion Language Models One-Step Generative Modeling Flow-Based Generative Modeling Generative Flow Networks Language Model Distillation

Feb 17, 2026

MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching

Molecular crystal structure prediction represents a grand challenge in computational chemistry due to large sizes of constituent molecules and complex intra- and intermolecular interactions. While generative modeling has revolutionized structure discovery for molecules, inorganic solids, and metal-organic frameworks, extending such approaches to fully periodic molecular crystals is still elusive. Here, we present MolCrystalFlow, a flow-based generative model for molecular crystal structure prediction. The framework disentangles intramolecular complexity from intermolecular packing by embedding molecules as rigid bodies and jointly learning the lattice matrix, molecular orientations, and centroid positions. Centroids and orientations are represented on their native Riemannian manifolds, allowing geodesic flow construction and graph neural network operations that respects geometric symmetries. We benchmark our model against a state-of-the-art generative model (MOFFlow) for large-size periodic crystals and a rule-based structure generation method (Genarris) on two open-source molecular crystal datasets. MolCrystalFlow outperforms MOFFlow while achieving competitive performance against Genarris. We also demonstrate an integration of MolCrystalFlow model with universal machine learning potential to accelerate molecular crystal structure prediction, paving the way for data-driven generative discovery of molecular crystals.

Cheng Zeng, Harry W. Sullivan, Thomas Egg +8

Department of Chemistry, University of Florida, Gainesville, FL 32611, USA · Quantum Theory Project, University of Florida, Gainesville, FL 32611, USA · Department of Chemical Engineering and Material Science, University of Minnesota - Twin Cities, Minneapolis, MN 55455, USA +6

Crystal Structure Prediction Flow-Based Generative Modeling Flow Matching

Feb 17, 2026

Verifier-Constrained Flow Expansion for Discovery Beyond the Data

Flow and diffusion models are typically pre-trained on limited available data (e.g., molecular samples), covering only a fraction of the valid design space (e.g., the full molecular space). As a consequence, they tend to generate samples from only a narrow portion of the feasible domain. This is a fundamental limitation for scientific discovery applications, where one typically aims to sample valid designs beyond the available data distribution. To this end, we address the challenge of leveraging access to a verifier (e.g., an atomic bonds checker), to adapt a pre-trained flow model so that its induced density expands beyond regions of high data availability, while preserving samples validity. We introduce formal notions of strong and weak verifiers and propose algorithmic frameworks for global and local flow expansion via probability-space optimization. Then, we present Flow Expander (FE), a scalable mirror descent scheme that provably tackles both problems by verifier-constrained entropy maximization over the flow process noised state space. Next, we provide a thorough theoretical analysis of the proposed method, and state convergence guarantees under both idealized and general assumptions. Ultimately, we empirically evaluate our method on both illustrative, yet visually interpretable settings, and on a molecular design task showcasing the ability of FE to expand a pre-trained flow model increasing conformer diversity while preserving validity.

Riccardo De Santi, Kimon Protopapas, Ya-Ping Hsieh +1

ETH Zürich · ETH AI Center

Flow-Based Generative Modeling Constrained Generative Modeling

Feb 17, 2026

Constraining Streaming Flow Models for Adapting Learned Robot Trajectory Distributions

Robot motion distributions often exhibit multi-modality and require flexible generative models for accurate representation. Streaming Flow Policies (SFPs) have recently emerged as a powerful paradigm for generating robot trajectories by integrating learned velocity fields directly in action space, enabling smooth and reactive control. However, existing formulations lack mechanisms for adapting trajectories post-training to enforce safety and task-specific constraints. We propose Constraint-Aware Streaming Flow (CASF), a framework that augments streaming flow policies with constraint-dependent metrics that reshape the learned velocity field during execution. CASF models each constraint, defined in either the robot's workspace or configuration space, as a differentiable distance function that is converted into a local metric and pulled back into the robot's control space. Far from restricted regions, the resulting metric reduces to the identity; near constraint boundaries, it smoothly attenuates or redirects motion, effectively deforming the underlying flow to maintain safety. This allows trajectories to be adapted in real time, ensuring that robot actions respect joint limits, avoid collisions, and remain within feasible workspaces, while preserving the multi-modal and reactive properties of streaming flow policies. We demonstrate CASF in simulated and real-world manipulation tasks, showing that it produces constraint-satisfying trajectories that remain smooth, feasible, and dynamically consistent, outperforming standard post-hoc projection baselines.

Jieting Long, Dechuan Liu, Weidong Cai +2

School of Computer Science, The University of Sydney, Australia. · School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Australia. · Australian Center For Robotics, The University of Sydney, Australia. +1

Robot Motion Generation Constrained Motion Planning Flow-Based Generative Modeling

Feb 16, 2026

Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under

S_n \times SE(3)

symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.

Cai Zhou, Zijie Chen, Zian Li +7

Massachusetts Institute of Technology · Zhejiang University · Peking University +3

Generative Modeling Diffusion Models 3D Molecular Generation Molecular Graph Generation Flow-Based Generative Modeling

Feb 13, 2026

Native Extrapolation Awareness in Flow-Based Conditional Generation

The ability of Flow Matching (FM) to model complex conditional distributions has established it as the state-of-the-art for prediction tasks (e.g., robotics, weather forecasting). However, deployment in safety-critical settings is hindered by a critical extrapolation hazard: driven by smoothness biases, flow models yield plausible outputs even for off-manifold conditions, resulting in silent failures indistinguishable from valid predictions. In this work, we introduce Diverging Flows, a novel approach that enables a single model to simultaneously perform conditional generation and native extrapolation detection by structurally enforcing inefficient transport for off-manifold inputs. We evaluate our method on synthetic manifolds, cross-domain style transfer, and weather temperature forecasting, demonstrating that it achieves effective detection of extrapolations without compromising predictive fidelity or inference latency. These results establish Diverging Flows as a robust solution for trustworthy flow models, paving the way for reliable deployment in domains such as medicine, robotics, and climate science.

Constantinos Tsakonas, Serena Ivaldi, Jean-Baptiste Mouret

Inria, Université de Lorraine, CNRS, Loria Nancy, France

Flow Matching Flow-Based Generative Modeling OOD Detection Conditional Generative Modeling

Feb 12, 2026

FAIL: Flow Matching Adversarial Imitation Learning for Image Generation

Post-training of flow matching models-aligning the output distribution with a high-quality target-is mathematically equivalent to imitation learning. While Supervised Fine-Tuning mimics expert demonstrations effectively, it cannot correct policy drift in unseen states. Preference optimization methods address this but require costly preference pairs or reward modeling. We propose Flow Matching Adversarial Imitation Learning (FAIL), which minimizes policy-expert divergence through adversarial training without explicit rewards or pairwise comparisons. We derive two algorithms: FAIL-PD exploits differentiable ODE solvers for low-variance pathwise gradients, while FAIL-PG provides a black-box alternative for discrete or computationally constrained settings. Fine-tuning FLUX with only 13,000 demonstrations from Nano Banana pro, FAIL achieves competitive performance on prompt following and aesthetic benchmarks. Furthermore, the framework generalizes effectively to discrete image and video generation, and functions as a robust regularizer to mitigate reward hacking in reward-based optimization. Code and data are available at https://github.com/HansPolo113/FAIL.

Yeyao Ma, Chen Li, Xiaosong Zhang +2

Shanghai Jiao Tong University · Xi’an Jiaotong University · Tencent

Flow Matching Conditional Image Generation Adversarial Imitation Learning Imitation Learning Flow-Based Generative Modeling

Feb 11, 2026

Dual-End Consistency Model

The slow iterative sampling nature remains a major bottleneck for the practical deployment of diffusion and flow-based generative models. While consistency models (CMs) represent a state-of-the-art distillation-based approach for efficient generation, their large-scale application is still limited by two key issues: training instability and inflexible sampling. Existing methods seek to mitigate these problems through architectural adjustments or regularized objectives, yet overlook the critical reliance on trajectory selection. In this work, we first conduct an analysis on these two limitations: training instability originates from loss divergence induced by unstable self-supervised term, whereas sampling inflexibility arises from error accumulation. Based on these insights and analysis, we propose the Dual-End Consistency Model (DE-CM) that selects vital sub-trajectory clusters to achieve stable and effective training. DE-CM decomposes the PF-ODE trajectory and selects three critical sub-trajectories as optimization targets. Specifically, our approach leverages continuous-time CMs objectives to achieve few-step distillation and utilizes flow matching as a boundary regularizer to stabilize the training process. Furthermore, we propose a novel noise-to-noisy (N2N) mapping that can map noise to any point, thereby alleviating the error accumulation in the first step. Extensive experimental results show the effectiveness of our method: it achieves a state-of-the-art FID score of 1.70 in one-step generation on the ImageNet 256x256 dataset, outperforming existing CM-based one-step approaches.

Linwei Dong, Ruoyu Guo, Ge Bai +3

1Zhejiang University · 2Bytedance Inc. · 3Zhejiang Lab

One-Step Generative Modeling Consistency Distillation Diffusion-Based Image Generation Flow-Based Generative Modeling Consistency Models