@inproceedings{
sorrenson2024learning,
title={Learning Distributions on Manifolds with Free-Form Flows},
author={Peter Sorrenson and Felix Draxler and Armand Rousselot and Sander Hummerich and Ullrich Koethe},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=QbPHYPZKJI}
}
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.
Learning Distributions on Manifolds with Free-Form Flows
Peter Sorrenson Felix Draxler Armand Rousselot Sander Hummerich Ullrich Koethe