Particle Denoising Diffusion Sampler
Angus Phillips Hai-Dang Dau Michael John Hutchinson Valentin De Bortoli George Deligiannidis Arnaud Doucet
Denoising diffusion models have become ubiquitous for generative modeling.
The core idea is to transport the data distribution to a Gaussian by using a
diffusion. Approximate samples from the data distribution are then obtained by
estimating the time-reversal of this diffusion using score matching ideas. We
follow here a similar strategy to sample from unnormalized probability
densities and compute their normalizing constants. However, the time-reversed
diffusion is here simulated by using an original iterative particle scheme
relying on a novel score matching loss. Contrary to standard denoising
diffusion models, the resulting Particle Denoising Diffusion Sampler (PDDS)
provides asymptotically consistent estimates under mild assumptions. We
demonstrate PDDS on multimodal and high dimensional sampling tasks.