# Sharp comparisons between sliced and standard 1-Wasserstein distances

arXiv: https://arxiv.org/abs/2510.16465 · HTML: https://mlsanity.com/paper/2510.16465/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2025.

## Built on by (most cited first, 2 of 2)

- [Convergence Rates for Distribution Matching with Sliced Optimal Transport](https://mlsanity.com/paper/2602.10691/) (2026)
- [The Observable Wasserstein Distance](https://mlsanity.com/paper/2605.09916/) (2026)

## Abstract (arXiv)

Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative estimates between the sliced 1-Wasserstein distance and the 1-Wasserstein distance. We construct a concrete example to demonstrate the exponents in the estimate is sharp. We also provide a general analysis for the case where slicing involves projections onto k-planes and not just lines.