General Manifolds via Physics-Informed Neural Networks

Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks

arXiv:2605.31106v1 Announce Type: new Abstract: Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a...