Wasserstein Gradient Flows

Ask about this topic

Overview

Wasserstein gradient flows study distribution-valued dynamics that decrease an energy while moving probability mass according to optimal-transport geometry. Common tools include Otto calculus for deriving continuous-time equations, the Jordan–Kinderlehrer–Otto (JKO) scheme for implicit time steps, and particle or neural approximations for computation; Wasserstein–Fisher–Rao flows add mechanisms for mass creation and removal. These ideas support sampling and generative modeling, as well as policy optimization, inverse problems, and learning population dynamics. Convergence guarantees are strongest under conditions such as convexity or log-Sobolev inequalities, while multimodal sampling, finite-sample error, and whether practical algorithms faithfully realize the intended flow remain central challenges.

Latest papers

CardsList

44 papers8 papers in the last four weeks, up 167% on the four weeks before. 0.0% of all new papers.

  1. A Jump-Modified Wasserstein Gradient Flow for Maximum Mean Discrepancy with Energy Kernels

    Oct 21, 2026Ansh Desai, Jason Liu, Srujan Roplekar +1Wasserstein Gradient FlowsMaximum Mean Discrepancy

  2. Projected Wasserstein-Fisher-Rao Flows for Hawkes Background-Intensity Estimation

    Oct 14, 2026Isaias Banales, Arturo JaramilloHawkes ProcessesTemporal Point Processes

    Facultad de Ciencias, Universidad Aut´onoma de M´exico · Department of Probability and Statistics, Centro de Investigaci´on en Matem´aticas A.C., Guanajuato, M´exico

  3. Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme

    Oct 7, 2026Chenguang Duan, Johannes Hertrich, Gabriele SteidlSampling from Unnormalized DistributionsBoltzmann Sampling

    Institut für Geometrie und Praktische Mathematik, RWTH Aachen University · Institute of Computer Science, University of Göttingen · Institute of Mathematics, TU Berlin

  4. Finite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows

    Oct 7, 2026Ryotaro Kawata, Atsushi Nitanda, Taiji SuzukiWasserstein Gradient FlowsGradient Descent Dynamics

    The University of Tokyo · Agency for Science, Technology and Research (A*STAR) · Nanyang Technological University +1

  5. One-Step Generation via Riemannian Wasserstein Gradient Flows

    Oct 3, 2026David Li, Chanhyuk Lee, Jaehoon Yoo +7One-Step Generative ModelingWasserstein Gradient Flows

    Mohamed bin Zayed University of Artificial Intelligence · Korea Advanced Institute of Science and Technology (KAIST) · Applied AI Institute +3

  6. Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling

    Oct 1, 2026Daniel McBride, Pratik Khandagale, Cristina Garcia-Cardona +1Dynamical SystemsWasserstein Gradient Flows

    Los Alamos National Laboratory, Los Alamos, NM 87545, USA

  7. Discrete Wasserstein Flows for One-Step Generative Modeling

    Oct 1, 2026Alessandro Micheli, Andrea Zerio, Samir BhattWasserstein Gradient FlowsMarkov Chains

    Imperial College London London, United Kingdom · Department of Computer Science, Aalborg University, Copenhagen, Denmark; Centre for Frontier AI Research (CFAR), Institute of Advanced Intelligence and Computing (IAIC), A*STAR, Singapore · University of Copenhagen Copenhagen, Denmark

  8. RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows

    Sep 30, 2026Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn +1Wasserstein Gradient FlowsOne-Step Generative Modeling

    KAIST

  9. One-Step Generative Modeling via Unbalanced Optimal Transport

    Sep 26, 2026Yirong Shen, Mengfei Xia, Junpeng Jing +2One-Step Generative ModelingOptimal Transport

    Imperial College London · Ant Group · Brunel University of London

  10. Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energies

    Sep 22, 2026Zhengjiang Lin, Philippe RigolletWasserstein Gradient Flows

  11. Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows

    Sep 16, 2026Francesca Romana Crucinio, Sahani PathirajaWasserstein Gradient FlowsLog-Concave Sampling

    ESOMAS, University of Turin, Italy & Collegio Carlo Alberto, Turin, Italy · School of Mathematics & Statistics, UNSW Sydney, Australia

  12. Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

    Aug 12, 2026Thejani Gamage, Hyemin Gu, Zhizhen Zhang +3Wasserstein Gradient FlowsGenerative Modeling

    Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA · School of Data and Information Sciences (SDIS) and Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC

  13. Statistical Mechanics of Learning on Product Wasserstein Manifolds

    Aug 2, 2026Srinivasa Rao P Vangmayi P ReddyStatistical Physics of LearningWasserstein Gradient Flows

    Curlvee Technolabs, India; Former Scientist, C-DAC.

  14. Wasserstein Residuals: Learning Gradient Flows from Population Dynamics

    Jul 6, 2026Markus Heinonen, Yair Shenfeld, Ricardo Baptista +4Dynamical SystemsWasserstein Gradient Flows

    Basis Research Institute · Aalto University · Brown University +2

  15. The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space

    Jun 23, 2026Yian Yao, Weiwei ZhangFlow MatchingWasserstein Gradient Flows

    from the mortal world · from heaven

  16. A Unifying View of Variational Generative Wasserstein Flows

    May 29, 2026Paul Caucheteux, Clément Bonet, Anna KorbaWasserstein Gradient FlowsGenerative Modeling

    ENSAE, CREST, IP Paris · MAP, CNRS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France

  17. Global Convergence of Wasserstein Policy Gradient for Entropy-Regularized Reinforcement Learning

    May 25, 2026Zhaoyu Zhu, Rui Gao, Shuang LiOptimization Convergence AnalysisWasserstein Gradient Flows

    Shanghai Jiao Tong University · The University of Texas at Austin · The Chinese University of Hong Kong, Shenzhen

  18. A note on convergence of Wasserstein policy optimization

    May 21, 2026David Šiška, Yufei ZhangWasserstein Gradient FlowsPolicy Optimization

    School of Mathematics, University of Edinburgh, United Kingdom · Department of Mathematics, Imperial College London, United Kingdom

  19. A Unified Framework for Data-Free One-Step Sampling via Wasserstein Gradient Flows

    May 18, 2026Chenguang Wang, Tianshu YuWasserstein Gradient FlowsOne-Step Generative Modeling

    School of Data Science The Chinese University of Hong Kong, Shenzhen

  20. Training Infinitely Deep and Wide Transformers

    May 17, 2026Raphaël Barboni, Maarten V. de Hoop, Takashi Furuya +1TransformerWasserstein Gradient Flows

    Bocconi University · Rice University · Doshisha University, RIKEN AIP +1

  21. Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows

    May 15, 2026Alex Massucco, Leonardo Del Grande, Marcello Carioni +2TransformerTransformer Training Dynamics

    Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK · Department of Mathematics, University of Twente, Enschede, Netherlands

  22. One-Step Generative Modeling via Wasserstein Gradient Flows

    May 12, 2026Jiaqi Han, Puheng Li, Qiushan Guo +3Wasserstein Gradient FlowsImage Generation

    Stanford University · ByteDance

  23. Probability-Flow Distillation: Exact Wasserstein Gradient Flow for High-Fidelity 3D Generation

    May 9, 2026Rohith Ramanan, A. N. RajagopalanDiffusion Model DistillationWasserstein Gradient Flows

    Department of Physics Indian Institute of Technology Madras · Department of Electrical Engineering Indian Institute of Technology Madras

  24. Consistency Regularised Gradient Flows for Inverse Problems

    May 8, 2026Alessio Spagnoletti, Tim Y. J. Wang, Marcelo Pereyra +1Latent Diffusion ModelsWasserstein Gradient Flows

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

  25. Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow

    May 8, 2026Juil Koo, Mingue Park, Jiwon Choi +2Robot Policy LearningWasserstein Gradient Flows

    KAIST

  26. On the Wasserstein Gradient Flow Interpretation of Drifting Models

    May 6, 2026Arthur Gretton, Li Kevin Wenliang, Alexandre Galashov +3Wasserstein Gradient FlowsSinkhorn Divergence

    Google DeepMind

  27. Properties and limitations of geometric tempering for gradient flow dynamics

    Apr 22, 2026Francesca Romana Crucinio, Sahani PathirajaWasserstein Gradient Flows

    ESOMAS, University of Turin, Italy · Collegio Carlo Alberto, Turin, Italy · School of Mathematics & Statistics, UNSW Sydney, Australia

  28. A Wasserstein Geometric Framework for Hebbian Plasticity

    Apr 17, 2026Ulrich TanNeural Representation GeometryHebbian Learning

  29. Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization

    Apr 16, 2026Mathias DusReinforcement LearningWasserstein Gradient Flows

    IRMA

  30. Generative Path-Finding Method for Wasserstein Gradient Flow

    Apr 13, 2026Chengyu Liu, Xiang ZhouFokker–Planck EquationWasserstein Gradient Flows

    Department of Data Science, City University of Hong Kong, Kowloon, Hong Kong SAR · Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR