Abstract

This talk will survey recent work, by me and others, on the use of diffusion models as amortised variational posteriors. While diffusion models are classically trained to maximise a variational bound on dataset likelihood, their expressive power can also be harnessed to approximate posterior distributions over latent variables where no unbiased samples are available – that is, amortised Bayesian inference – and to approximately solve the related problem of sampling posteriors under diffusion model priors. The ensuing learning problem has close connections to stochastic optimal control and can be solved using a variety of learning-based and Monte Carlo approaches. After introducing these algorithms and connections, I will present recent results on the use of techniques from deep reinforcement learning in diffusion sampling and on connections with (twisted) sequential Monte Carlo. Applications include high-dimensional inverse problems in astrophysics and biology, constrained sampling in large generative models, inference of stochastic dynamical systems, and black-box Bayesian optimisation.