mlsanityData to 14 Oct 2026

Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernels

arXiv 2301.11624 ↗First posted 27 Jan 2023cs.LG math.OC math.PRcited by 9

Not on the map. Why?

Abstract (arXiv)

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the understanding of such flows. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot restrict ourselves to absolutely continuous measures, we have to deal with transport plans and velocity plans instead of usual transport maps and velocity fields. Indeed, we approximate the disintegration of both plans by generative NNs which are learned with respect to appropriate loss functions. In order to evaluate the quality of both neural schemes, we benchmark them on the interaction energy. Here we provide analytic formulas for Wasserstein schemes starting at a Dirac measure and show their convergence as the time step size tends to zero. Finally, we illustrate our neural MMD flows by numerical examples.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 30 of its 54 references that are in the map. First posted on arXiv 27 Jan 2023.

Builds on

30 of 54 references.

References · 30

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18 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 4; 2025: 1; 2026: 1.

9 papers.

  1. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 37
  2. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  3. 2024Deep MMD Gradient Flow without adversarial trainingcited by 19
  4. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flowscited by 12
  5. 2024Fast Kernel Summation in High Dimensions via Slicing and Fourier Transformscited by 8
  6. 2024Kernel Semi-Implicit Variational Inferencecited by 8
  7. 2024Importance Corrected Neural JKO Samplingcited by 7
  8. 2023Manifold learning in Wasserstein spacecited by 6
  9. 2026A Kernel Approach for Semi-implicit Variational Inferencecited by 1