mlsanityData to 7 Oct 2026

Forward-Euler time-discretization for Wasserstein gradient flows can be wrong

arXiv 2406.08209 ↗First posted 12 Jun 2024stat.ML cs.LG math.OCcited by 3

Not on the map. Why?

Abstract (arXiv)

In this note, we examine the forward-Euler discretization for simulating Wasserstein gradient flows. We provide two counter-examples showcasing the failure of this discretization even for a simple case where the energy functional is defined as the KL divergence against some nicely structured probability densities. A simple explanation of this failure is also discussed.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 10 of its 24 references that are in the map. First posted on arXiv 12 Jun 2024.

Builds on

10 of 24 references.

References · 10

  1. 2015Learning with a Wasserstein Losscited by 194
  2. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 182
  3. 2021Large-Scale Wasserstein Gradient Flowscited by 76
  4. 2021Projected Wasserstein gradient descent for high-dimensional Bayesian inferencecited by 24
  5. 2020Dataset Dynamics via Gradient Flows in Probability Spacecited by 18
  6. 2024Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spacescited by 15
  7. 2023MonoFlow: Rethinking Divergence GANs via the Perspective of Wasserstein Gradient Flowscited by 12
  8. 2023Estimating the Rate-Distortion Function by Wasserstein Gradient Descentcited by 5
  9. 2023High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systemscited by 1
  10. 2024Wasserstein gradient flow for optimal probability measure decompositioncited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 1.

3 papers.

  1. 2024Linear convergence of proximal descent schemes on the Wasserstein spacecited by 3
  2. 2024Using Linearized Optimal Transport to Predict the Evolution of Stochastic Particle Systemscited by 0
  3. 2026Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimizationcited by 0