# Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions

arXiv: https://arxiv.org/abs/2503.16580 · HTML: https://mlsanity.com/paper/2503.16580/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2025.

## Abstract (arXiv)

We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This distance is defined by penalizing the action with a costless movement of the particle that does not change the direction and speed of its trajectory. We show that for Gaussian distribution resume to measuring the Euclidean distance between their ordered vector of eigenvalues and we show a direct application in recovering Latent Gaussian distributions.