Learning Distributions on Manifolds with Free-Form Flows

• URL: http://arxiv.org/abs/2312.09852v3
• Date: Mon, 25 Nov 2024 10:47:11 GMT
• Title: Learning Distributions on Manifolds with Free-Form Flows
• Authors: Peter Sorrenson, Felix Draxler, Armand Rousselot, Sander Hummerich, Ullrich Köthe,
• Abstract summary: We propose Manifold Free-Form Flows (M-FFF), a simple new generative model for data on manifold. M-FFF is straightforwardly adapted to any manifold with a known projection. It consistently matches or outperforms previous single-step methods.
• Score: 7.773439780305304
• License: http://creativecommons.org/licenses/by/4.0/
• 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. It is typically two orders of magnitude faster than multi-step methods based on diffusion or flow matching, achieving better likelihoods in several experiments. We provide our code at https://github.com/vislearn/FFF.

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