Title: Neural Diffusion 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.