  We propose conformal generative modeling, a framework for generative modeling
on 2D surfaces approximated by discrete triangle meshes. Our approach leverages
advances in discrete conformal geometry to develop a map from a source triangle
mesh to a target triangle mesh of a simple manifold such as a sphere. After
accounting for errors due to the mesh discretization, we can use any generative
modeling approach developed for simple manifolds as a plug-and-play subroutine.
We demonstrate our framework on multiple complicated manifolds and multiple
generative modeling subroutines, where we show that our approach can learn good
estimates of distributions on meshes from samples, and can also learn
simultaneously from multiple distinct meshes of the same underlying manifold.
