Manifold Diffusion Fields
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.
647011f4cc049b49e360ebe2
Ahmed A. Elhag
647011f4cc049b49e360ebe3
Joshua M. Susskind
claimed_verified
2023-05-26T17:15:06.115Z
6470d2247fd7ecdbd0ec3cc9
/avatars/52c5eca12499a1aa9bd49c43d4f20685.svg
Joshua M. Susskind
user
jsusskind
647011f4cc049b49e360ebe4
Miguel Angel Bautista
Manifold Diffusion Fields
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.
Manifold Diffusion Fields (MDF) learns generative models of continuous functions on Riemannian manifolds using eigen-functions of the Laplace-Beltrami Operator, achieving better diversity and fidelity.
Manifold Diffusion Fields MDF Riemannian manifolds spectral geometry analysis intrinsic coordinate system Laplace-Beltrami Operator continuous functions sample continuous functions rigid transformations isometric transformations