  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. We make our code public at
https://github.com/vislearn/FFF.
