  Wasserstein barycenters provide a geometric notion of the weighted average of
probability measures based on optimal transport. In this paper, we present a
scalable algorithm to compute Wasserstein-2 barycenters given sample access to
the input measures, which are not restricted to being discrete. While past
approaches rely on entropic or quadratic regularization, we employ input convex
neural networks and cycle-consistency regularization to avoid introducing bias.
As a result, our approach does not resort to minimax optimization. We provide
theoretical analysis on error bounds as well as empirical evidence of the
effectiveness of the proposed approach in low-dimensional qualitative scenarios
and high-dimensional quantitative experiments.
