Spectral Diffusion Processes

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.

Modeling Information Diffusion in Online Social Networks with Partial Differential Equations

“…To deal with the mesh-dependent issue, we propose to carry out the diffusion learning over an appropriate latent space [20], e.g., over the Fourier space [13] or the spectral space [19]. Alternatively, we can take advantage of the cascaded diffusion model pipeline to make predictions on a fine mesh based on a model pre-trained on a coarse mesh [9].…”