Spectral Diffusion Processes

TL;DR

This paper extends score-based generative modeling to functional spaces by spectral representation and dimensionality reduction, enabling effective sampling of complex functional data.

Contribution

It introduces a novel spectral diffusion approach for functional data, combining spectral representation with finite-dimensional score-based models.

Findings

Effective modeling of multimodal functional datasets

Successful spectral diffusion over functional spaces

Dimensionality reduction facilitates scalable sampling

Abstract

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To do so, we represent functional data in spectral space to dissociate the stochastic part of the processes from their space-time part. Using dimensionality reduction techniques we then sample from their stochastic component using finite dimensional SGM. We demonstrate our method's effectiveness for modelling various multimodal datasets.