Learning to Generate Wasserstein Barycenters

TL;DR

This paper introduces a deep learning method that significantly accelerates the computation of Wasserstein barycenters, enabling real-time applications in image processing and color transfer.

Contribution

A neural network-based approach that speeds up Wasserstein barycenter computation by 60 times, generalizing well to multiple measures and large-scale images.

Findings

Achieves millisecond computation times on large images.

Outperforms state-of-the-art methods by a factor of 60.

Effectively transfers colors between images.

Abstract

Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the problem of finding measures in-between given input measures in the optimal transport sense -- is even more computationally demanding as it requires to solve an optimization problem involving optimal transport distances. By training a deep convolutional neural network, we improve by a factor of 60 the computational speed of Wasserstein barycenters over the fastest state-of-the-art approach on the GPU, resulting in milliseconds computational times on $512\times512$ regular grids. We show that our network, trained on Wasserstein barycenters of pairs of measures, generalizes well to the problem of finding Wasserstein barycenters of more than two measures. We demonstrate the efficiency of our approach for computing barycenters of sketches and transferring colors between multiple images.