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.
@article{arxiv.2209.14125,
title = {Spectral Diffusion Processes},
author = {Angus Phillips and Thomas Seror and Michael Hutchinson and Valentin De Bortoli and Arnaud Doucet and Emile Mathieu},
journal= {arXiv preprint arXiv:2209.14125},
year = {2022}
}
Comments
17 pages, 11 figures, Score-based Method Workshop at 36th Conference on Neural Information Processing Systems (NeurIPS 2022)