# Sliced Wasserstein distance between probability measures on Hilbert spaces

arXiv: https://arxiv.org/abs/2307.05802 · HTML: https://mlsanity.com/paper/2307.05802/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2023.

## Built on by (most cited first, 5 of 5)

- [Mesh-Informed Neural Operator : A Transformer Generative Approach](https://mlsanity.com/paper/2506.16656/) (2025)
- [Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variates](https://mlsanity.com/paper/2402.01493/) (2024)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHS](https://mlsanity.com/paper/2405.13153/) (2024)
- [Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing](https://mlsanity.com/paper/2510.04579/) (2025)

## Abstract (arXiv)

The sliced Wasserstein distance as well as its variants have been widely considered in comparing probability measures defined on mathbb Rd. Here we derive the notion of sliced Wasserstein distance for measures on an infinite dimensional separable Hilbert spaces, depict the relation between sliced Wasserstein distance and narrow convergence of measures and quantize the approximation via empirical measures.