Learning Distributions on Manifolds with Free-Form Flows
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910711198777344 |
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| author | Sorrenson, Peter Draxler, Felix Rousselot, Armand Hummerich, Sander Köthe, Ullrich |
| author_facet | Sorrenson, Peter Draxler, Felix Rousselot, Armand Hummerich, Sander Köthe, Ullrich |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09852 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning Distributions on Manifolds with Free-Form Flows Sorrenson, Peter Draxler, Felix Rousselot, Armand Hummerich, Sander Köthe, Ullrich Machine Learning 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. |
| title | Learning Distributions on Manifolds with Free-Form Flows |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2312.09852 |