  Modeling distributions on Riemannian manifolds is a crucial component in
understanding non-Euclidean data that arises, e.g., in physics and geology. The
budding approaches in this space are limited by representational and
computational tradeoffs. We propose and study a class of flows that uses convex
potentials from Riemannian optimal transport. These are universal and can model
distributions on any compact Riemannian manifold without requiring domain
knowledge of the manifold to be integrated into the architecture. We
demonstrate that these flows can model standard distributions on spheres, and
tori, on synthetic and geological data. Our source code is freely available
online at http://github.com/facebookresearch/rcpm
