Learning to Generate Wasserstein Barycenters

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 of finding measures in-between given input the optimal sense—are even more computationally demanding it requires an optimization involving distances. By training deep convolutional neural network, we improve by factor 80 computational speed barycenters over fastest state-of-the-art approach on GPU, resulting milliseconds times $$512\times 512$$ regular grids. We show that our trained pairs measures, generalizes well than two measures. demonstrate efficiency computing sketches and transferring colors between multiple images.