Flow Models

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3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 39

Oct 1, 2026cs.LG

Flowing Faster to Coordinate: One-Step Online Multi-Agent Flow Policies

Multi-agent reinforcement learning (MARL) provides a powerful framework for learning coordinated behaviors through interactions with the environment. Developing MARL policies requires balancing expressive modeling of complex and multimodal action distributions with efficient training and execution. Generative policies, particularly diffusionbased policies, can faithfully capture complex and multimodal behaviors, but costly iterative sampling hinders their scalability in online multi-agent settings. We propose an Online MARL framework via one-step Flow model (OMAF) that combines expressive generative policies with efficient one-step action generation. OMAF employs a Transformer-based flow policy to capture complex coordination behaviors, while its approximate path score surrogate provides a principled route to synchronized flow policy optimization. To enable stable and sampleefficient learning, we further develop a joint optimization scheme coupling softmax Q-value estimation with a joint flow policy objective for coordinated policy learning. By eliminating iterative sampling, OMAF dramatically reduces training overhead without sacrificing policy expressiveness. Extensive experiments across 10 standard tasks from MPE and MAMuJoCo show that OMAF consistently achieves superior performance, with up to 3.4x higher returns and 10.5x sample efficiency improvement compared with baseline methods. These results validate the effectiveness of OMAF as an expressive and computationally efficient one-step flow policy paradigm for online MARL.

Zhuoran Li, Yunzhan Li, Xun Wang +2

Institute for Interdisciplinary Information Sciences, Tsinghua University · Engineering Systems and Design Pillar, Singapore University of Technology and Design

Multi-Agent Reinforcement Learning Flow Policies Multimodal Action Distributions Flow Models

Sep 30, 2026cs.CV

Multimodal Flow: Unified Flow Modeling of Language and Vision in Embedding Spaces

We present Multimodal Flow, a fully continuous generative model of language and vision. Most unified multimodal models either model both language and quantized images as discrete tokens or combine discrete language prediction with continuous image generation. The former introduces a visual quantization bottleneck. The latter requires modality-dependent objectives and sampling procedures. Fully continuous modeling avoids these trade-offs and enables a shared generative process, but remains underexplored for multimodal pretraining. Multimodal Flow introduces a unified continuous architecture that integrates multimodal continuous representations with a shared chunk-causal flow backbone. It organizes text blocks and images as ordered continuous hyperchunks, preserving textual token order and visual spatial structure. The backbone learns a single vector field over these hyperchunks through Flow Matching. Joint attention enables cross-modal interaction, while modality-specific feed-forward networks process each modality. The model predicts multiple target chunks in parallel during training and generates hyperchunks sequentially at inference. We instantiate MF-1 and pretrain it on multimodal data. Across 0.6B, 1.2B, and 1.6B scales, continued pretraining consistently improves multimodal modeling. With only 150B pretraining tokens, MF-1 achieves an average score of 82.8 across GenEval and DPG-Bench and 75.3 across VQAv2, MMBench, and POPE, remaining competitive with unified models trained on substantially more data. Under matched data, optimization, and parameter budgets, Multimodal Flow further outperforms representative hybrid and discrete models. These results establish continuous chunk-based embedding flow modeling as a new fully continuous paradigm for unified multimodal modeling. The related code and model are publicly released at https://github.com/hustvl/Multimodal-Flow.

Hongyuan Tao, Xinggang Wang, Lianghui Zhu +7

Huazhong University of Science and Technology · Beijing Jiaotong University · Horizon Robotics

Multimodal Pretraining Multimodal Representations Flow Models Generative Models

Sep 28, 2026cs.CV

CapField-OPD: Learning Continuous Capability Fields via Joint-Anchored Multi-Teacher On-Policy Distillation for Flow Models

Reward-specialized post-training produces strong experts for flow-based generative models, while multi-teacher on-policy distillation (OPD) consolidates their capabilities into a single student. Existing methods, however, route each prompt to a single teacher according to its semantic category, implicitly binding the desired capability to prompt content. This coupling makes capability invocation vulnerable to prompt perturbations and prevents users from explicitly adjusting the strength of the desired capability at inference time. In this work, we introduce CapField-OPD, an OPD framework that integrates multiple teachers into a continuous capability field through explicit capability coordinates. We use teacher models as anchors to construct this field, with the coordinates determining how their outputs are combined. Each capability configuration thus receives a unique supervision target, and capability control no longer depends on prompt semantics. Since the training anchors may not be optimal at inference time, we further profile the learned field on a small calibration set. The coordinate with the highest mean reward serves as the recommended default, while coordinates that are frequently optimal offer a promising candidate set for test-time scaling. Extensive experiments on compositional generation, text rendering, and visual aesthetics demonstrate that CapField-OPD consolidates multiple specialized teachers into a single student while preserving or surpassing their performance, reliably invokes the desired capabilities under semantics-preserving prompt variations, and supports continuous capability control and coordinate-based test-time scaling.

Pengyang Ling, Jiazi Bu, Yujie Zhou +6

University of Science and Technology of China · Shanghai Jiao Tong University · Fudan University +2

Aware Heterogeneous Multi-Teacher Multimodal On-Policy Distillation Generative Flow Networks Uni-Opd Flow Models

Sep 27, 2026cs.LG

Elucidating the Design Space of Regression-based Diffusion Reinforcement Learning

A nascent family of methods that forgoes the policy gradient and reweights a supervised regression instead has garnered momentum in reinforcement learning for diffusion and flow models. DiffusionNFT, FlowAWR, and RAM are representative regimes with contrasting motivations. It is yet opaque what, if anything, they share. We substantiate that each is the solution of one divergence-constrained reward-maximization problem, and they are differentiated only by the convex generator that defines the constraint. Under the unified modeling framework, we unravel the relaxations that prior art made during building the advantage-embedded regression target: approximating the KKT condition and posterior normalizer for the linear and exponential tilt shapes DiffusionNFT and FlowAWR respectively, while preserving the exact sparsemax projection onto the probability simplex for linear tilt leads to another superior model type in this work. Beyond the theoretical underpinnings, we further empirically investigate the design space and shed light on the training recipe for regression-style diffusion RL. Retaining the merits discovered during our exploration gives rise to DiffusionRFT, our paradigm that converges faster, trains more stably, and attains the top performance.

Toyota Li, David Zhao, Alan Zhao

Tencent

Diffusion-Based Reinforcement Learning Methods Reward Gradients Reward-Only Policy Optimization Variants Flow Models Policy Gradient

Sep 14, 2026cs.LG

Learning Multimodal One-step Flow Policy via Value-weighted Optimal Transport

Offline reinforcement learning aims to learn a policy solely from fixed datasets, which often contain multimodal action distributions. Flow policies can naturally represent such multimodal behaviors, but learning an efficient one-step flow policy remains challenging: standard value guidance often leads to mode collapse or exploits overestimation bias in out-of-distribution regions. To address this, we introduce One-step Flow policy via Optimal Transport (OptiFlow), a framework for one-step flow policy learning as a structured sample-allocation problem. OptiFlow jointly trains a value-aware reference flow policy and an efficient one-step policy, coupling their action samples through state-wise entropic optimal transport. For each state, critic-estimated values define the priority of distillation target actions, while the action-distance cost ensures geometrically compatible pairings. By avoiding direct critic maximization, our transport-guided approach enables in-distribution exploitation by anchoring the one-step policy to high-value, dataset-supported modes without the risk of out-of-distribution divergence. Experimental results demonstrate that OptiFlow effectively captures optimal multimodal behaviors and achieves strong performance across diverse offline RL benchmarks. Our code is available at https://github.com/Yonsei-DILLab/OptiFlow.

Jaehun Shon, Jinha Choi, Jongwook Jeon +1

Department of Artificial Intelligence, Yonsei University

Flow Policies Multimodal Action Distributions Offline Reinforcement Learning Flow Models

Sep 9, 2026stat.ML

FlowCPO: A Unified Divergence View of Preference Alignment for Flow Models

Preference alignment for flow and diffusion models now spans online reinforcement learning and offline preference optimization, but the relation between these methods remains unclear. In particular, existing forward-process alignment methods require fresh samples from the current model, while offline methods based on fixed preference pairs rely primarily on positive-only fine-tuning or DPO-style likelihood-ratio surrogates. We organize these approaches through a divergence-based framework and introduce FlowCPO, an offline forward-KL objective that uses both preferred and dispreferred samples without online rollouts. For linear interpolation, we show under explicit regularity conditions that the forward-KL objective is bounded by a contrastive flow matching loss, yielding a tractable surrogate on fixed data. We further show that this loss is nonnegative, whereas the signed regression loss of simplified FlowDPO can be unbounded below. In the in-domain setting, FlowCPO achieves higher mean GenEval and OCR scores than the evaluated baselines, reaching 0.84 and 0.87 versus 0.81 and 0.74 for FlowDPO at CFG 3.0. In the out-of-domain setting, the results are mixed, with the best GenEval result but lower reward scores than RFT on several metrics.

Yansen Han, Shengyi Liao, Peng Sun +4

Westlake University · Zhejiang University · Kling Team, Kuaishou Technology

Flow Models Preference Alignment Diffusion Alignment Kullback-Leibler Divergence

Aug 7, 2026cs.CV

Multiple Hypothesis Flow Estimation for Video Frame Interpolation under Matching Ambiguity

Many flow-based video frame interpolation (VFI) methods synthesize an intermediate frame by estimating optical flow fields, warping the two input frames, and blending the warped observations. These latent flow fields are typically learned through image-level reconstruction supervision without direct flow annotations. In ambiguous regions containing repetitive or stochastic textures, rotating symmetric structures, or fast motion with blur, the matching evidence for a single query may contain multiple comparable and spatially separated peaks. Although the ground-truth intermediate frame provides indirect supervision, it may not uniquely identify the latent correspondence in ambiguous regions.When several locations provide multiple plausible matches, a single-flow estimator can retain only one displacement and discard the remaining candidates. If the selected match is incorrect or inconsistent with those of neighboring pixels, warping samples content from mismatched locations, producing ghosting, structural distortion, or blur.To address this limitation, we propose a multiple hypothesis flow estimation framework that preserves top-K candidate correspondences and selects one per location through a reliability-guided router. Each hypothesis is initialized from a coarse matching anchor and refined separately through anchor-centered local attention. Frame synthesis is thus conditioned on one selected flow-appearance hypothesis rather than a soft combination of candidate motions.Experiments on the proposed MA-HD benchmark and public VFI benchmarks show that our method achieves the best LPIPS and DISTS among the compared methods.

Zibo Su, Jing Kong, Ruixing Wang +2

1Xidian University · 2DJI Technology Co., Ltd.

Optical Flow Video Restoration Flow Models Interpolation Mismatch Hypothesis

Aug 5, 2026cs.CV

Poly-OPD: Heterogeneous Multi-Teacher On-Policy Distillation for Capability-Selectable Flow Models

Leading open text-to-image models often carry complementary strengths: one may lead on preference-aligned aesthetics while another follows compositional instructions more faithfully. However, differences in their autoencoders and noise schedules make it difficult to transfer these strengths across models. In this paper, we present Poly-OPD, a framework that can consolidate complementary strengths of heterogeneous teachers into a single compact flow-matching student. To bridge the incompatible latent spaces of different teachers, Poly-OPD performs on-policy distillation through a pixel bridge. Each student-generated image is re-encoded by a selected teacher's encoder and refined from a noise level matched by magnitude under the teacher's noise schedule. The resulting target is further matched to the student in frozen DINOv2 space, enabling supervision across incompatible latent spaces. To retain complementary capabilities without cross-teacher interference, Poly-OPD uses a gradient compatibility diagnostic to organize its adapters: attention LoRA modules are shared across teachers, whereas feed-forward adapters remain teacher-specific. During distillation, a gap-aware curriculum devotes more training to compositional categories where the student still falls short of the teacher. As each gap narrows, training shifts toward categories with larger remaining gaps. By distilling FLUX.1-dev and Z-Image into a 2.5B SD3.5-Medium student, Poly-OPD improves GenEval from 67.3 to 73.3, surpassing both larger teachers, and raises DrawBench HPSv3 from 9.34 to 11.35, consolidating both strengths within a switchable model.

Siming Fu, Haojun Xu, Ruizhe He +9

1Joy Future Academy · 2Zhejiang University · 3Beihang University

Aware Heterogeneous Multi-Teacher Multimodal On-Policy Distillation Uni-Opd Modern Text-To-Image Models Flow Models Image Generation Curriculum

Jul 29, 2026cs.LG

Flow Map Learning via Nongradient Vector Flow

Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration. Consistency models address this by directly learning the flow maps along the ODE trajectory, opening a design space between one-step and many-step approaches. However, existing methods face computational challenges such as requiring model inverses or backpropagation through iterated model calls, and do not always prove that the desired ODE flow map is a solution to the loss. We introduce SGFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration. SGFlow trains a model to compute both the ODE solutions and the implied velocity from scratch by following non-conservative dynamics with a stationary point at the desired flow map. On the CIFAR image benchmark, no single method attains the best FID at every step count: SGFlow attains the best FID at 10 sampling steps and remains competitive with flow matching, Meanflow, and Lagrangian map matching at other step counts, while being the only one with a proven stationary-point guarantee for its stopgrad-based dynamics.

Mark Goldstein, Anshuk Uppal, Raghav Singhal +2

Center for Computational Mathematics, Flatiron Institute. · Department of Applied Mathematics and Computer Science, Technical University of Denmark. · Courant Institute, New York University.

Flow Map Invertible Flows Flow Models

Jul 27, 2026cs.LG

FlowCTS: On-policy Continuous Trajectory Supervision of Flow Models

While on-policy distillation (OPD) effectively addresses sparse rewards and exposure bias in large language model post-training, its extension to flow models remains underexplored. To this end, we propose Flow Continuous Trajectory Supervision (FlowCTS), which matches subsequent student and reference trajectories initialized from the same student-visited state. Using the integral relation between trajectories and velocity fields, we derive a temporally weighted velocity-matching upper bound and discretize it into practical objectives parameterized by the number of supervision steps. Under a multi-reference setup, single-state FlowCTS-OPD outperforms vanilla KL-based OPD with faster convergence. FlowCTS-OPD improves GenEval from 0.90 to 0.93, OCR from 0.90 to 0.92, and PickScore from 22.75 to 23.06, while outperforming a mixed-reward RL baseline across all target metrics. Further analysis reveals a clear temporal supervision mismatch in vanilla KL-based OPD arising from its auxiliary SDE transition kernels. Beyond on-policy setting,FlowCTS also consistently outperforms vanilla SFT , particularly on OCR, while increasing supervision steps exhibit a trade-off between richer trajectory information and greater optimization difficulty.

Kaiyang Ye, Yuan Ge, Junxiang Zhang +8

Northeastern University · NiuTrans Research · Kunming University of Science and Technology

Flow Models Token-Level Supervision Uni-Opd

Jul 8, 2026eess.SP

Stability of Flow Models for Graph Signals

Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation. In this paper, we analyze continuous normalized flow models parameterized by GNNs and show that permutation equivariance is preserved for both the resulting continuous-time ordinary differential equations and their discrete numerical approximations used as graph signal samplers. Our primary contribution is to derive explicit stability bounds on the generated probability distributions, which quantify how relative graph perturbations affect the final sampled signals. Motivated by these theoretical bounds, we introduce a stability-promoting regularized flow matching strategy that actively penalizes the spatial Lipschitz constant of the vector field during model training. Experiments using synthetic smooth signals on stochastic block model graphs and real-world fMRI signals on brain connectomes demonstrate that this bound-oriented approach yields generative models that are more robust to structural noise, without sacrificing output quality.

Martin Schmidt, Gonzalo Mateos

Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA

Generative Flow Networks Flow Models Rotation Equivariance Functional Magnetic Resonance Imaging

Jul 3, 2026cs.LG

OpFlow: Learning Opportunity-Conditioned Choice Potentials for Robust OD Flow Prediction

Origin-destination (OD) flow prediction is central to urban analytics, yet deep models trained on raw counts remain vulnerable to distribution shift. The core problem is that raw count supervision cannot distinguish transferable choice mechanisms from environment-specific shortcuts. Raw OD count mixes two objects: how much demand an origin produces and how that demand is allocated across destinations. We argue that the transferable object is the exposure-to-choice law that maps spatial conditions to relative destination preferences. We propose OpFlow, a mechanism-constrained framework that learns row-centered choice potentials and reconstructs flows by combining the induced allocation with a separately calibrated origin scale. Under distribution shift, spatial exposures and the induced allocations are allowed to vary; what transfers is the conditional map from exposure states to relative choice potentials. Theoretically, we characterize the identifiable row-centered potential and show that classical spatial interaction laws are restricted log-potential cases. Controlled synthetic shifts and a real-world experiment show OpFlow improves robustness under environment shifts.

Changjian Liu, Yong Gao, Yuqing Wang +5

School of Earth and Space Sciences Peking University China, CN 100871 · College of Artificial Intelligence Zhejiang University China, CN 310027

Origin Destination Flows Flow Models Distribution Shifts Accurate Traffic Forecasting Discrete Choice Models Optical Flow+2

Jul 1, 2026cs.AI

PedNStream: Scalable Network Flow Simulation for Pedestrian Traffic Management

Large-scale crowd management requires pedestrian simulations that are both computationally efficient and compatible with feedback-based control. However, most open-source tools are either microscopic or not designed for network-scale closed-loop evaluation. This paper presents PedNStream (Pedestrian Network Flow Simulation), an open-source, Python-native simulator for macroscopic pedestrian network loading based on the Link Transmission Model (LTM). The framework extends LTM-based pedestrian models by incorporating stochastic link dynamics that capture diffusion and activity-induced variability, and replaces dynamic user equilibrium route choice with a utility-based formulation suited to uncertain, intervention-driven settings. PedNStream is implemented as a modular framework with built-in controller interfaces for interventions such as gating, flow separation, and route guidance. We evaluate the framework in a staged manner. Synthetic scenarios verify key mechanisms, including queue formation, spillback, congestion dissipation, and adaptive rerouting. Real-network experiments assess large-scale behavior and consistency with observed pedestrian counts. A closed-loop case study demonstrates controller integration, and a runtime analysis quantifies scalability. These results establish PedNStream as an efficient and practical testbed for large-scale pedestrian network simulation and control.

Weiming Mai, Dorine Duives, Serge Hoogendoorn

Department of Transportation and Planning, Delft University of Technology, Delft, Netherlands

Microscopic Traffic Simulations Flow Models Streaming Bellman Equation

Jun 29, 2026cs.RO

OpenSPM: An Environment-Transferable Robotic Key Spatial Pose Memory and Closed-Loop High-Frequency Flow-Matching Action Generation Model

Open-environment tabletop robotic manipulation requires systems to possess semantic understanding, precise geometric pose estimation, and high-frequency action generation. While end-to-end vision-language-action (VLA) models excel at semantic generalization, they often lack explicit geometric constraints for fine-grained tasks and require costly training. To bridge the gap between high-level semantics and low-level physical execution, we propose OpenSPM, an open environment spatial persistent memory framework consisting of spatial pose memory and flow-matching action generation model. OpenSPM first leverages semantically conditioned 3D perception and Kalman filtering to track continuous 6D poses. It then extracts key spatial poses from human demonstrations, keeping them as transferable, object-centric spatial persistent memory entries. During inference, OpenSPM retrieves relevant memory entries in terms of natural language instructions, transfers the spatial poses to new scenes using SE(3) transformations, and generates high-frequency action chunks via a lightweight conditional flow-matching model. Combined with real-time proprioceptive state feedback and terminal residual correction, the system effectively suppresses trajectory error accumulation. Evaluated on ten LIBERO-GOAL tasks, OpenSPM achieves an 85.6% success rate and an equivalent control frequency of 1033.3 Hz, while requiring minimal inference AI computing power. Extensive ablations illustrate that structured spatial persistent memory and closed-loop residual correction play a crucial role in reliable, high-frequency robotic manipulation.

Iok Tong Lei, Qingchen Xie, Yifan Wang +2

Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China · Institute for Artificial Intelligence, Tsinghua University, Beijing 100084, China

Robotic Manipulation Action Generation Flow Models High-Frequency Reconstruction

Jun 27, 2026physics.med-ph

An Optimal Contact-Mechanically Consistent and Flow-Separation Adapted Modeling of Vocal Fold Dynamics

Single mass-spring-damper models of vocal folds have been effective in simulating vocal fold vibrations without added complexity. However, single-degree-of-freedom models cannot sustain oscillation in the presence of structural damping unless source-tract interaction is considered. Moreover, existing lumped models struggle to accurately simulate vocal fold closure during phonation. This study aims to develop a reliable and simplified single-degree-of-freedom model of phonation that can simulate sustained oscillation in a damped system without incorporating a vocal tract model. Additionally, the proposed model maintains vocal fold closure in a manner consistent with the physics of phonation, addressing a longstanding challenge in existing lumped models. High-speed videoendoscopy (HSV) data from four normophonic subjects producing sustained vowel /i/ were used to extract glottal area waveforms (GAWs) via deep learning-based image segmentation for particle swarm optimization of the model parameters. An additional resistance force was incorporated to compensate for flow separation and generate the force imbalance required for sustained oscillation. An external structural force was also added during closure to sustain the closed phase. The 4th-order Runge-Kutta method was used to solve the governing equations with enhanced numerical stability and accuracy. The model parameters were optimized for individual subjects, resulting in normalized errors below 3% between experimental and simulated GAWs. The proposed model accurately reproduced subject-specific vocal fold vibrations and vocal fold closure in agreement with experimental data. Overall, the proposed model provides a computationally efficient framework for simulating sustained phonation without requiring complex source-tract coupling while capturing the key biomechanical and aerodynamic mechanisms of phonation.

Sardar Nafis Bin Ali, Maryam Naghibolhosseini, Mohsen Zayernouri

Department of Mechanical Engineering, Michigan State University, 428 S. Shaw Lane, East Lansing, 48824, MI, USA. · Department of Communicative Sciences and Disorders, Michigan State University, 1026 Red Cedar Rd, East Lansing, 48824, MI, USA.

Vocal Tract Shape Vocalizations Inverted Pendulum Flow Models

Jun 26, 2026cs.CV

Physics-Grounded Disentangled Flow Modeling for Brain Disease Progression Trajectory

Forecasting longitudinal brain lesion evolution is critical for disease monitoring and treatment planning. Existing approaches typically learn a direct mapping from a baseline image to a future observation, without explicitly modeling the physical mechanisms underlying the lesion progression. Such an entangled modeling of structural deformation and image intensity variation limits physical plausibility, model generalization, and interpretability. To address this, we propose PDF, a Physics-grounded Disentangled Flow matching framework for longitudinal brain disease forecasting. We explicitly decompose the longitudinal modeling of lesion growth into two processes, each learned by a dedicated flow matching network: morphology evolution, which captures lesion growth and structural deformation; and intensity evolution, which models signal changes driven by variations in lesion concentration. To enforce physics-grounded constraints, we introduce a PDE-regularized loss based on lesion growth dynamics, that enforces a diffusion-reaction-advection formulation for morphological evolution. Experiments on three public longitudinal datasets spanning diverse brain diseases demonstrate state-of-the-art performance, validating the effectiveness of the disentangled modeling framework and physics-grounded learning design. Code is publicly available at https://github.com/jhuldr/PDF.

Jun Wang, Peirong Liu

Department of Electrical and Computer Engineering, Data Science and AI Institute, Johns Hopkins University

Longitudinal Imaging Disease Flow Models Conditional Flow Matching One-Dimensional Viscous Burgers Equation Entanglement

Jun 25, 2026cs.CV

Don't Settle at the Mode! Mitigating Diversity Collapse in Pretrained Flow Models via Feature Self-Guidance

State-of-the-art flow models generate stunning images from text or image prompts. However, they suffer from diversity collapse when generating multiple samples under the same conditioning. Existing methods address this issue via either latent guidance, which has limited effectiveness, or sample selection, which relies on external reward models that incur significant inference-time overhead. In this work, we introduce an efficient, training-free self-guidance mechanism to mitigate diversity collapse without requiring additional reward models. Specifically, we disperse the internal features of the flow model during batch generation with feature self-guidance. Further, to keep the features close to the manifold, we introduce a manifold regularization step that projects these dispersed features back onto the data manifold, ensuring diverse generation without sacrificing alignment with the input conditions. Our method integrates seamlessly as a plug-and-play module into pretrained flow models, adding only a marginal inference cost. Experiments demonstrate significant improvements in diversity while preserving fidelity across several conditional flow models, including multi-step and few-step text-to-image, depth-to-image, and reference image generation.

Pradhaan S Bhat, Rishubh Parihar, Abhijnya Bhat +1

Indian Institute of Science · Stanford University

Generative Flow Networks Diversity Collapse Flow Models

Jun 8, 2026cs.AI

DynaOD: Dynamic Origin-Destination Flow Generation with Discrete-to-Continuous Temporal Semantic Modeling

Dynamic origin-destination (OD) flow generation seeks to synthesize realistic mobility dynamics from temporal context alone, without relying on historical OD observations. A key challenge is to translate semantic temporal signals into temporally coherent OD patterns while preserving the inherent spatial heterogeneity of urban regions. We propose DynaOD, a semantic-driven framework that models temporal dynamics through two complementary perspectives: discrete directional trends that characterize qualitative shifts in urban activity patterns, and continuous temporal evolution that captures how such shifts unfold over time. By jointly encoding these temporal semantics, the framework constructs time-varying region representations that condition pretrained static OD generators in a lightweight and plug-and-play fashion. This modular design further supports scalable deployment and cross-city transferability. Extensive experiments on large-scale real-world datasets show that our method consistently outperforms representative baselines in both predictive accuracy and distributional fidelity. Code is publicly available at https://github.com/csjiezhao/DynaOD.

Jie Zhao, Xianqi Dai, Jie Feng +2

Department of Electronic Engineering, BNRist, Tsinghua University · Tsinghua Shenzhen International Graduate School · Zhongguancun Academy

Origin Destination Flows Temporal Dynamics Accurate Traffic Forecasting Flow Models Dynawm

Jun 7, 2026cs.LG

Active Flow Expansion for Out-of-Distribution Discovery: from Theory to Molecules

Standard flow and diffusion pre-training matches the distribution of available data (e.g., molecules), which often covers only a small fraction of the valid design space. In generative discovery, however, one aims to sample valid new-to-nature designs, assigned negligible probability under, and thus inaccessible to, standard models fitted to the observed data. To overcome this limitation, we depart from data distribution matching and view a generative model through its generable set: the region it covers with non-negligible probability. This allows to introduce a new learning principle for out-of-distribution flow modeling: enlarging a model's generable set to increase coverage of the valid design space. We propose Active Flow Expansion (ActFlow), a continued pre-training method that employs verifier feedback to expand a pre-trained model over new valid regions by iteratively adapting to synthetic data generated through active exploration in the learned flow representation. Theoretically, we establish to our knowledge first-of-their-kind statistical learning guarantees for out-of-distribution flow modeling, analyzing generable set expansion as a local-to-global reachability process over a learned representation. Empirically, we assess ActFlow with suitable out-of-distribution generative modeling metrics across small organic molecules, mid-sized drug-like molecules, therapeutic peptides, and protein sequence design tasks. Results show that ActFlow expands valid coverage far beyond the region modeled by the initial pre-trained model, significantly outperforming widely adopted synthetic flow pre-training methods.

Riccardo De Santi, Bruce Lee, Cristian Perez Jensen +6

ETH Zurich ETH AI Center · University of Pennsylvania · Caltech FutureHouse

Generative Flow Networks Flow Models Drug Design Out-Of-Distribution Detection Molecules Theory

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

Flow Models Rectified Flow Offline Reinforcement Learning Loss Function Least Squares

May 22, 2026cs.CV

VDE: Training-Free Accelerating Rectified Flow Model via Velocity Decomposition and Estimation

Though rectified flow models have achieved remarkable performance in image, video, and 3D generation, their practical deployments are challenged by slow inference speeds. Prior acceleration methods reuse cached features from previous steps, which neglects the growing mismatch between static caches and the evolving input, leading to reduced output fidelity. This work proposes Velocity Decomposition and Estimation (VDE), a training-free acceleration method that shifts the paradigm from caching-and-reusing to decomposing-and-estimating. Specifically, VDE decomposes the model's velocity into components parallel and orthogonal to the input, exploiting their temporal predictability and directional stability for precise, input-adaptive estimation. To prevent error accumulation, it periodically anchors the model's state via full forward passes. Extensive experiments on image and video generation tasks demonstrate that VDE achieves substantial acceleration with minimal loss in visual quality. Notably, VDE accelerates Flux by 3.22 times and achieves an LPIPS of 0.069 on Qwen-Image, outperforming the best baseline with a 52.2% reduction.

Junwen Tan, Jinglin Liang, Hongyuan Chen +1

South China University of Technology

Rectified Flow Conditional Velocity Flow Models Video Generation

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

Flow Models Geometric Guidance Guidance Generative Quality

May 18, 2026physics.data-an

A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery

Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of physical, engineered, and data-driven systems. The objective of this work is to establish a unified perspective on such systems, to identify modeling approaches that balance expressivity, interpretability, computational complexity, and data requirements, and to investigate how highly expressive models can be used to uncover the dominant mechanisms underlying observed dynamics. Starting from the Helmholtz-Hodge decomposition of continuous vector fields, we review the recently proposed Graph Vector Field (GVF) framework and its discrete representation on simplicial complexes. We then introduce a hierarchy of alternative approaches, including parametric conditional models, linear graph dynamical systems, and reduced Hodge representations. Finally, we propose a verification and validation methodology based on benchmark datasets from well-understood physical systems and on systematic model-reduction and ablation studies. The resulting family of structured-flow models within a common framework, ranging from low-dimensional parametric representations to full GVF formulations, supports a diagnostic methodology in which gradient, curl, harmonic, and topological contributions are systematically assessed through ablation studies. This process enables the identification of dominant mechanisms underlying the observed dynamics and guides the construction of simplified models tailored to the available data and operational constraints. By separating structural verification, behavioral verification, and domain-specific validation, the proposed approach provides a foundation for scalable and interpretable analysis of complex dynamical systems across multiple application domains.

Diego Casadei

Fly High Engineering AG, Badenerstrasse 13, 5200 Brugg AG, Switzerland

Vector Fields Flow Models Model Discovery Unified Framework

May 17, 2026cs.MA

Human-Flow Digital Twin for Predicting the Effects of Mobility Introduction on Visitor Circulation

We propose a framework for predicting the effects of mobility introduction measures using a human-flow digital twin. This digital twin incorporates a multi-agent simulator that can represent how visitors choose destinations depending on factors such as their current location and the attractiveness of spots. We extract data on how visitors selected destinations with respect to measured pre-intervention human-flow data, inter-spot distances, spot attractiveness, and travel volumes, and use these data to train each agent's decision model of this simulator. The trained decision model is a function that takes a visitor's current state and surrounding environmental information as input and outputs which spot the visitor will move toward next. By expressing mobility introduction measures as changes to inter-point distances or to spot attractiveness, the framework can reproduce human flows with mobility introduction in the multi-agent simulator and thereby quantify effects such as changes in visitor counts and circulation. We evaluated the proposed method using human-flow data measured with and without introducing mobility within Wakayama Castle Park in Japan. When reproducing flows with mobility introduction using a multi-layer perceptron decision model, the cosine similarity of the spatial population distribution exceeded 0.7, confirming that the approach can replicate the flow changes caused by the mobility introduction.

Chiharu Shima, Haruki Yonekura, Fukuharu Tanaka +2

bitA Inc., Shinagawa-ku, Tokyo, Japan · The University of Osaka, Suita, Osaka, Japan · RIKEN Center for Computational Science, Kobe, Hyogo, Japan

Mobility Cognitive Digital Twins Flow Models Multi-Agent Simulations Analytics Impact Analysis

May 15, 2026cs.CV

Embedding-perturbed Exploration Preference Optimization for Flow Models

Recent advancements have established Reinforcement Learning (RL) as a pivotal paradigm for aligning generative models with human intent. However, group-based optimization frameworks (e.g., GRPO) face a critical limitation: the rapid decay of intra-group variance. As the distinctiveness among samples within a group diminishes, the variance approaches zero. This eliminates the very learning signal required for optimization, rendering the process unstable and forcing the policy into premature stagnation or reward hacking. Existing strategies, such as varying the initial noise or increasing group sizes, often fail to address this fundamental issue, resulting in training instability or diminishing returns. To overcome these challenges, we propose

\textbf{Embedding-perturbed Exploration Preference Optimization (}E^2\textbf{PO)}

, a novel framework that sustains optimization through embedding-level perturbation. Our method introduces structured, embedding-level perturbations within sample groups, guaranteeing a robust variance that preserves the discriminative signal throughout the training process. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art baselines, achieving a more faithful alignment with human preference.

Sujie Hu, Chubin Chen, Jiashu Zhu +3

1Tsinghua University · ⋆Work done during the internship at AMAP · 2AMAP, Alibaba Group

Stochastic Exploration Flow Models Exploration Variance

May 13, 2026cs.CV

Asymmetric Flow Models

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

\times

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

Hansheng Chen, Jan Ackermann, Minseo Kim +2

Stanford University

Latent Flow Flow Models Velocity Field

May 10, 2026cs.LG

dFlowGRPO: Rate-Aware Policy Optimization for Discrete Flow Models

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

Zhengyan Wan, Yidong Ouyang, Panwen Hu +1

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

Flow Models Diffusion-Based Reinforcement Learning Methods Diffusion Models Frictive Policy Optimization Flow-Grpo

May 9, 2026cs.CV

Restoration-Aligned Generative Flow Models for Blind Motion Deblurring

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

\times

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

Insoo Kim, Jinwoo Shin

1NAVER Cloud · 2KAIST AI

Gaussian Deblurring Flow Models Generative Flow Networks Vision Datasets Motion

May 9, 2026cs.CV

FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priors

Plug-and-play (PnP) methods for solving inverse problems have recently achieved strong performance by leveraging denoising priors based on powerful generative diffusion and flow models. However, existing diffusion- and flow-based PnP methods typically rely on stochastic renoise-denoise operations, which complicate the analysis of their convergence behavior. In this work, we identify and formalize the deterministic renoise-denoise operator underlying flow-based plug-and-play methods. This perspective reveals that these methods implicitly define a deterministic operator given by the expectation of a denoiser over the latent noise distribution. Building on this insight, we propose FlowADMM, a PnP algorithm that integrates the renoise-denoise operator into the classical alternating direction method of multiplier (ADMM) framework. We establish convergence guarantees for FlowADMM under weak Lipschitz conditions on the underlying flow network, and extend the analysis to non-stationary time schedules. Empirically, FlowADMM achieves state-of-the-art performance among flow-based PnP methods on a range of inverse problems, including denoising, deblurring, super-resolution, and inpainting, while requiring fewer data consistency evaluations than prior approaches.

Hendrik Sommerhoff, Michael Moeller

Computer Vision Group, University of Siegen Hölderlinstraße 3, 57076 Siegen, Germany

Bayesian Inverse Problems Iterative Denoising Methods Inverse Problem Alternating Direction Method Of Multiplier Flow Models Plug-And-Play

May 8, 2026cs.LG

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

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

Kim Yong Tan, Yueming Lyu, Ivor Tsang +1

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

Generative Flow Networks Flow Models Guidance Vector Fields Training-Free Efficient Planning+1

May 7, 2026cs.AI

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

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

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

Flow Models Generative Flow Networks Adjoint Matching Feature Alignment Model Fine-Tuning Artificial Intelligence Alignment

May 7, 2026cs.LG

RepFlow: Representation Enhanced Flow Matching for Causal Effect Estimation

Estimating causal effects from observational data has become increasingly critical in diverse fields including healthcare, economics, and social policy. The fundamental challenge in causal inference arises from the missing counterfactuals and the selection bias. Existing methods are largely limited to point estimates and lack the capacity for distribution modeling. In this work, we propose RepFlow, a novel framework that formulates causal effect estimation as a joint optimization problem integrating representation learning with Conditional Flow Matching (CFM). RepFlow mitigates selection bias by minimizing the entropically regularized Wasserstein distance between treated and control representations. To enhance numerical stability, we further introduce an

L_2

normalization constraint on latent representations. This balanced representation enables the flow model to accurately capture the distribution of potential outcomes. Extensive experiments across a wide range of benchmarks demonstrate that RepFlow consistently outperforms existing methods in both point and distributional causal effect estimation.

Yifei Xie, Jian Huang

Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University, Hong Kong, China.

Causal Inferences Selection Bias Flow Models Representation Learning

May 5, 2026cs.LG

A Few-Step Generative Model on Cumulative Flow Maps

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

Zhiqi Li, Duowen Chen, Yuchen Sun +1

Georgia Institute of Technology, Atlanta, United States of America

Flow Map Flow Models Generative Models Latent Transport

Apr 30, 2026stat.ML

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

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

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

Microsoft Research New England · Harvard University, Kempner Institute

Generative Flow Networks Adjoint Matching Flow Models Generative Models Model Fine-Tuning Stochastic Optimal Control+1

Apr 17, 2026cs.LG

Neuro-Symbolic ODE Discovery with Latent Grammar Flow

Understanding natural and engineered systems often relies on symbolic formulations, such as differential equations, which provide interpretability and transferability beyond black-box models. We introduce Latent Grammar Flow (LGF), a neuro-symbolic generative framework for discovering ordinary differential equations from data. LGF embeds equations as grammar-based representations into a discrete latent space and forces semantically similar equations to be positioned closer together with a behavioural loss. Then, a discrete flow model guides the sampling process to recursively generate candidate equations that best fit the observed data. Domain knowledge and constraints, such as stability, can be either embedded into the rules or used as conditional predictors.

Karin Yu, Eleni Chatzi, Georgios Kissas

Institute of Structural Engineering, ETH Zurich, Zurich, Switzerland · ETH AI Center, ETH Zurich, Zurich, Switzerland · Swiss Data Science Center, Zurich, Switzerland

Neuro-Symbolic Framework Latent Flow Flow Models Discovery

Mar 15, 2026cs.LG

Trust-Region Noise Search for Black-Box Alignment of Diffusion and Flow Models

Optimizing the noise samples of diffusion and flow models is an increasingly popular approach to align these models to target rewards at inference time. However, we observe that these approaches are usually restricted to differentiable or cheap reward models, the formulation of the underlying pretrained generative model, or are memory/compute inefficient. We instead propose a simple trust-region based search algorithm (TRS) which treats the pre-trained generative and reward models as a black-box and only optimizes the source noise. Our approach achieves a good balance between global exploration and local exploitation, and is versatile and easily adaptable to various generative settings and reward models with minimal hyperparameter tuning. We evaluate TRS across text-to-image, molecule and protein design tasks, and obtain significantly improved output samples over the base generative models and other inference-time alignment approaches which optimize the source noise sample, or even the entire reverse-time sampling noise trajectories in the case of diffusion models. Our source code is publicly available.

Niklas Schweiger, Daniel Cremers, Karnik Ram

Technical University of Munich, Germany · Munich Center for Machine Learning, Germany

Diffusion Alignment Generative Flow Networks Generative Models Flow Models Trust Region

Feb 23, 2026cs.LG

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

Flow Models Classifier-Free Guidance Geometric Guidance Guidance Imagenet

Feb 13, 2026cs.LG

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 Models Extrapolation Text-Conditioned Diffusion Model Conditional Distribution Manifolds

Feb 9, 2026eess.IV

Trajectory Stitching for Solving Inverse Problems with Flow-Based Models

Flow-based generative models have emerged as powerful priors for solving inverse problems. One option is to directly optimize the initial latent code (noise), such that the flow output solves the inverse problem. However, this requires backpropagating through the entire generative trajectory, incurring high memory costs and numerical instability. We propose MS-Flow, which represents the trajectory as a sequence of intermediate latent states rather than a single initial code. By enforcing the flow dynamics locally and coupling segments through trajectory-matching penalties, MS-Flow alternates between updating intermediate latent states and enforcing consistency with observed data. This reduces memory consumption while improving reconstruction quality. We demonstrate the effectiveness of MS-Flow over existing methods on image recovery and inverse problems, including inpainting, super-resolution, and computed tomography.

Alexander Denker, Zeljko Kereta, Carola-Bibiane Schönlieb +1

Department of Computer Science, University College London · Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

Flow Models Inverse Problem Intermediate Latent States