mlsanityData to 7 Oct 2026

Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions

arXiv 2602.05227 ↗First posted 5 Feb 2026stat.ML cs.LG cs.NAcited by 1

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Abstract (arXiv)

Gradient flows of the Kullback--Leibler (KL) divergence, such as the Fokker--Planck equation and Stein Variational Gradient Descent, evolve a distribution toward a target density known only up to a normalizing constant. We introduce new gradient flows of the KL divergence with a remarkable combination of properties: they admit accurate interacting-particle approximations in high dimensions, and the per-step cost scales linearly in both the number of particles and the dimension. These gradient flows are based on new transportation-based Riemannian geometries on the space of probability measures: the Radon--Wasserstein geometry and the related Regularized Radon--Wasserstein (RRW) geometry. We define these geometries using the Radon transform so that the gradient-flow velocities depend only on one-dimensional projections. This yields interacting-particle-based algorithms whose per-step cost follows from efficient Fast Fourier Transform-based evaluation of the required 1D convolutions. We additionally provide numerical experiments that study the performance of the proposed algorithms and compare convergence behavior and quantization. Finally, we prove some theoretical results including well-posedness of the flows and long-time convergence guarantees for the RRW flow.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 31 of its 74 references that are in the map. First posted on arXiv 5 Feb 2026.

Builds on

31 of 74 references.

References · 31

  1. 2016Variational Inference: A Review for Statisticianscited by 1,466
  2. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  3. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  4. 2017Advances in Variational Inferencecited by 236
  5. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  6. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  7. 2020Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimationcited by 87
  8. 2022Variational inference via Wasserstein gradient flowscited by 84
  9. 2019On the geometry of Stein variational gradient descentcited by 82
  10. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  11. 2022Probability flow solution of the Fokker-Planck equationcited by 46
  12. 2019Accelerating Langevin Sampling with Birth-deathcited by 45
19 more
  1. 2018Scaling limit of the Stein variational gradient descent: the mean field regimecited by 35
  2. 2021Challenges and Opportunities in High-dimensional Variational Inferencecited by 35
  3. 2020Projected Stein Variational Gradient Descentcited by 33
  4. 2021Projected Wasserstein gradient descent for high-dimensional Bayesian inferencecited by 24
  5. 2020Sliced Kernelized Stein Discrepancycited by 23
  6. 2021A Survey of Monte Carlo Methods for Parameter Estimationcited by 23
  7. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  8. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  9. 2022Self-Consistency of the Fokker-Planck Equationcited by 18
  10. 2022Regularized Stein Variational Gradient Flowcited by 18
  11. 2023On the Convergence of Coordinate Ascent Variational Inferencecited by 18
  12. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  13. 2018Stein Variational Gradient Descent as Moment Matchingcited by 15
  14. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  15. 2023Deep learning probability flows and entropy production rates in active mattercited by 15
  16. 2024Convergence of coordinate ascent variational inference for log-concave measures via optimal transportcited by 13
  17. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
  18. 2022Grassmann Stein Variational Gradient Descentcited by 12
  19. 2024Convergence rate of random scan Coordinate Ascent Variational Inference under log-concavitycited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Barron Optimal Transport I: Generative Modelingcited by 0