Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.20498 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and stochastic issues that are absent in the Euclidean setting. In this work, we develop a diffusion modeling framework defined directly on finite-dimensional spherical harmonic representations of real-valued functions on the sphere. We show that the spherical discrete Fourier transform maps spatial Brownian motion to a constrained Gaussian process in the frequency domain with deterministic, generally non-isotropic covariance. This induces modified forward and reverse-time stochastic differential equations in the spectral domain. As a consequence, spatial and spectral score matching objectives are no longer equivalent, even in the band-limited setting, and the frequency-domain formulation introduces a geometry-dependent inductive bias. We derive the corresponding diffusion equations and characterize the induced noise covariance.