Spectral Diffusion Processes

Angus Phillips, Thomas Seror, Michael John Hutchinson, Valentin De Bortoli, Arnaud Doucet, Emile Mathieu

Keywords: Functional data, stochastic processes, neural processes, Gaussian processes, score-based generative modelling, diffusion models, spectral decomposition

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.

Student Paper: Yes

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2209.14125/code)