RESEARCH

Riemannian Continuous Normalizing Flows

November 20, 2020

Abstract

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, tori, 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.

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AUTHORS

Written by

Maximilian Nickel

Emile Mathieu

Publisher

NeurIPS

Research Topics

Computer Vision

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