  Normalizing flows have shown great promise for modelling flexible probability
distributions in a computationally tractable way. However, whilst data is often
naturally described on Riemannian manifolds such as spheres, torii, and
hyperbolic spaces, most normalizing flows implicitly assume a flat geometry,
making them either misspecified or ill-suited in these situations. To overcome
this problem, we introduce Riemannian continuous normalizing flows, a model
which admits the parametrization of flexible probability measures on smooth
manifolds by defining flows as the solution to ordinary differential equations.
We show that this approach can lead to substantial improvements on both
synthetic and real-world data when compared to standard flows or previously
introduced projected flows.
