Flow Map Learning

Also known as MAP

Flow map learning studies how to predict a system’s finite-time transition—from one state or distribution to another—rather than repeatedly integrating a local velocity field. Approaches include semigroup-consistency objectives such as MeanFlow, optimal-transport flow matching, stochastic flow maps for SDEs, and distillation of slow teachers into few-step generators; neural operators and physical or geometric constraints adapt the idea to PDEs, molecular dynamics, and control. Applications range from one-step image and text generation to long-horizon forecasting, inverse problems, and molecular simulation. A central tension is making large, few-step transitions accurate and stable while preserving physical structure and generalization across step sizes or unseen conditions; theory for training stability and out-of-distribution behavior remains uneven.

Latest papers

49 papers11 papers in the last four weeks, up 22% on the four weeks before. 0.1% of all new papers.

Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps
Jun 27, 2026RuiKang OuYang, Hanlin Yu, Xinyue Ai +7Flow Map Learning Generative Modeling
University of Cambridge · University of Helsinki · Peking University +3
Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems
Jun 18, 2026Nicolas Zilberstein, Morteza Mardani, Santiago SegarraFlow Matching Flow Map Learning
Rice University · NVIDIA Inc.
Itô maps for any-step SDEs
Jun 9, 2026Zhengkai Pan, Peter Potaptchik, Wenxi Yao +2Stochastic Differential Equations Diffusion Distillation
Harvard University · University of Oxford · Kempner Institute
Multimarginal flow matching with optimal transport potentials
Jun 3, 2026Raghav Kansal, David Crair, Nghia Nguyen +2Flow Matching Flow Map Learning
Bexorg, Inc., New Haven, CT, USA.
Strong Stochastic Flow Maps
May 31, 2026Sam McCallum, Zander W. Blasingame, Timothy Herschell +3Stochastic Differential Equations Few-Step Diffusion Sampling
University of Bath · 2AITHYRA
Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error
May 29, 2026Markus GrossKoopman Operator Learning Nonlinear System Identification
Institute for AI Safety and Security, German Aerospace Center (DLR), Sankt Augustin and Ulm, Germany
LC-Flow: Learning Local Continuous Optical Flow and Confidence from events
May 23, 2026Gunwoo Jeon, Chaesong Park, Jongwoo LimOptical Flow Event-Based Vision
IPAI, Seoul National University
Path-independent Flow Matching for Multi-parameter Generative Dynamics
May 13, 2026Francisco Téllez, AmirHossein Zamani, Philippe Martin +5Flow Matching Flow Map Learning
Université de Montréal, Mila · Concordia University, Mila · Concordia University +2
Scaling Categorical Flow Maps
May 8, 2026Oscar Davis, Anastasiia Filippova, Pierre Ablin +4Language Model Scaling Flow Map Learning
Apple · University of Oxford
Semantically Stable Image Composition Analysis via Saliency and Gradient Vector Flow Fusion
Apr 14, 2026Armin Dadras, Robert Sablatnig, Franziska Proksa +1Flow Map Learning
Computer Vision Lab, TU Wien Vienna, Austria · UAS St. Pölten St. Pölten, Austria
Discrete Flow Maps
Apr 10, 2026Peter Potaptchik, Jason Yim, Adhi Saravanan +3Flow Map Learning Non-Autoregressive Text Generation
Harvard University · University of Oxford · Independent +3
ODE-free Neural Flow Matching for One-Step Generative Modeling
Apr 7, 2026Xiao ShouOne-Step Generative Modeling Flow Matching
Baylor University
SBF: An Effective Representation to Augment Skeleton for Video-based Human Action Recognition
Apr 4, 2026Zhuoxuan Peng, Yiyi Ding, Yang Lin +1Video Action Recognition Skeleton-Based Action Recognition
The Hong Kong University of Science and Technology · The Hong Kong University of Science and Technology (Guangzhou)
RHYME-XT: A Neural Operator for Spatiotemporal Control Systems
Mar 18, 2026Marijn Ruiter, Miguel Aguiar, Jake Rap +2PDE Surrogate Modeling PDE Operator Learning
Digital Futures and Division of Decision and Control Systems, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden. · Control Systems Group, EE Dept., Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Variational Flow Maps: Make Some Noise for One-Step Conditional Generation
Mar 7, 2026Abbas Mammadov, So Takao, Bohan Chen +4Conditional Generative Modeling One-Step Generative Modeling
Department of Statistics, University of Oxford · California Institute of Technology · University of Toronto +1
CoFL: Continuous Flow Fields for Language-Conditioned Navigation
Mar 3, 2026Haokun Liu, Zhaoqi Ma, Yicheng Chen +5Vision-Language Navigation Flow Map Learning
A Monte Carlo estimator of flow fields for sampling and noise problems
Feb 27, 2026Michael S. Albergo, Gurtej KanwarLattice Field Theory High-Energy Physics
Society of Fellows, Harvard University 78 Mount Auburn St, Cambridge, MA United States · Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, EH9 3FD Edinburgh, United Kingdom
A Long-Short Flow-Map Perspective for Drifting Models
Feb 24, 2026Zhiqi Li, Bo ZhuDrifting Models Flow Map Learning
School of Interactive Computing, Georgia Institute of Technology
Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics
Jan 29, 2026Winfried Ripken, Michael Plainer, Gregor Lied +5Dynamical Systems Flow Map Learning
Technical University Berlin · BIFOLD · Free University of Berlin +6

Jun 27, 2026J/K move · Enter open · S save

Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps

RuiKang OuYang, Hanlin Yu, Xinyue Ai, Yutong He+6

University of Cambridge · University of Helsinki · Peking University+3

Flow Map Learning Generative Modeling Molecular Generation Flow-Based Generative Modeling

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Recent progress in flow-based generative modeling has led to models that output high-quality samples while using only a small number of function evaluations. However, at present, there is a lack of similar advances in estimating the model likelihood. In particular, most existing methods either rely on restrictive architectures that enable exact calculations, or use stochastic approximations such as Hutchinson's trace estimator that introduce substantial variance. In this work, we introduce SCAlable LikeLihood distillation of flOw maPs (SCALLOP). SCALLOP builds on the recently proposed F2D2, a likelihood flow map model that can generate samples and their densities in a small number of function evaluations. While F2D2 uses Hutchinson's estimator during training, we introduce an alternative and more scalable likelihood distillation objective that is Hutchinson-free and admits a vectorized formulation. Empirically, we demonstrate the effectiveness of SCALLOP as a Boltzmann generator in molecular science, and further validate its benefit on image datasets. SCALLOP significantly reduces both training variance and training time while consistently improving performance compared to F2D2, and is competitive with the state-of-the-art while achieving up to 10x inference speedup over the fastest baseline.