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Paper · 2312.09852 · NeurIPS · 2024

Learning Distributions on Manifolds with Free-Form Flows

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

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 7 functions out of this paper's own repositories and ran 6 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
vislearn/FFF canonical 6 of 7
FunctionStatusWhere it lives
build_model Ran vislearn/FFF/fff/base.py
code served (permissive licence) · get_code("615bdd56e7131c04")
get_module Ran vislearn/FFF/fff/model/utils.py
code served (permissive licence) · get_code("62beb8156e773f1e")
guess_image_shape Ran vislearn/FFF/fff/model/utils.py
code served (permissive licence) · get_code("b5063fada3aaa1f8")
make_dense Ran vislearn/FFF/fff/model/utils.py
code served (permissive licence) · get_code("505ce06e6c35e263")
rand_log_uniform Ran vislearn/FFF/fff/base.py
code served (permissive licence) · get_code("08ea55cee9bcbaa8")
soft_heaviside Ran vislearn/FFF/fff/base.py
code served (permissive licence) · get_code("dc02abdd7ec5f6ca")
make_res_net Not yet run vislearn/FFF/fff/model/res_net.py
code served (permissive licence) · get_code("bec3f11465bbb13c")

Repositories linked to this paper

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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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