Skip to yearly menu bar Skip to main content


Poster

Learning Distributions on Manifolds with Free-Form Flows

Peter Sorrenson · Felix Draxler · Armand Rousselot · Sander Hummerich · Ullrich Köthe

[ ]
Thu 12 Dec 11 a.m. PST — 2 p.m. PST

Abstract:

We propose Manifold Free-Form Flows (M-FFF), a simple new generative model for data on manifolds. The existing approaches to learning a distribution on arbitrary manifolds are expensive at inference time, since sampling requires solving a differential equation. Our method overcomes this limitation by sampling in a single function evaluation. The key innovation is to optimize a neural network via maximum likelihood on the manifold, possible by adapting the free-form flow framework to Riemannian manifolds. M-FFF is straightforwardly adapted to any manifold with a known projection. It consistently matches or outperforms previous single-step methods specialized to specific manifolds, and is competitive with multi-step methods with typically two orders of magnitude faster inference speed.

Live content is unavailable. Log in and register to view live content