Papers › Efficient Gradient Flows in Sliced-Wasserstein Space
Efficient Gradient Flows in Sliced-Wasserstein Space
Clément Bonet, Nicolas Courty, François Septier, Lucas Drumetz
Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows. To solve them numerically, a possible approach is to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to the proximal scheme in Euclidean spaces. However, it requires solving a nested optimization problem at each iteration, and is known for its computational challenges, especially in high dimension. To alleviate it, very recent works propose to approximate the JKO scheme leveraging Brenier's theorem, and using gradients of Input Convex Neural Networks to parameterize the density (JKO-ICNN). However, this method comes with a high computational cost and stability issues. Instead, this work proposes to use gradient flows in the space of probability measures endowed with the sliced-Wasserstein (SW) distance. We argue that this method is more flexible than JKO-ICNN, since SW enjoys a closed-form differentiable approximation. Thus, the density at each step can be parameterized by any generative model which alleviates the computational burden and makes it tractable in higher dimensions.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections