Neural Diffusion Processes

Vincent Dutordoir, Alan Saul, Zoubin Ghahramani, Fergus Simpson

Keywords: diffusion models, gaussian processes, neural processes, stochastic processes

TL;DR: Diffusion models for stochastic processes

Abstract: Gaussian processes provide an elegant framework for specifying prior and posterior distributions over functions. They are, however, also computationally expensive, and limited by the expressivity of their covariance function. We propose Neural Diffusion Processes (NDPs), a novel approach based upon diffusion models, that learns to sample from distributions over functions. Using a novel attention block we are able to incorporate properties of stochastic processes, such as exchangeability, directly into the NDP's architecture. We empirically show that NDPs are able to capture functional distributions that are close to the true Bayesian posterior. This enables a variety of downstream tasks, including hyperparameter marginalisation, non-Gaussian posteriors and global optimisation.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Probabilistic Methods (eg, variational inference, causal inference, Gaussian processes)

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/neural-diffusion-processes/code)