Manifold Diffusion Fields
Authors: name: Ahmed A. Elhag, name: Joshua M. Susskind, name: Miguel Angel Bautista

We present Manifold Diffusion Fields (MDF), an approach to learn generative
models of continuous functions defined over Riemannian manifolds. Leveraging
insights from spectral geometry analysis, we define an intrinsic coordinate
system on the manifold via the eigen-functions of the Laplace-Beltrami
Operator. MDF represents functions using an explicit parametrization formed by
a set of multiple input-output pairs. Our approach allows to sample continuous
functions on manifolds and is invariant with respect to rigid and isometric
transformations of the manifold. Empirical results on several datasets and
manifolds show that MDF can capture distributions of such functions with better
diversity and fidelity than previous approaches.