Spectral Diffusion Processes
This work addresses the challenge of generative modeling for functional data, which is an incremental extension of existing score-based methods to a new domain.
The authors tackled the problem of extending score-based generative modeling to functional spaces by representing functional data in spectral space and using dimensionality reduction to sample from the stochastic component with finite-dimensional methods, demonstrating effectiveness on multimodal datasets.
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.