Particle Denoising Diffusion Sampler

Denoising diffusion models have become ubiquitous for generative modeling.The core idea is to transport the data distribution to a Gaussian by using adiffusion. Approximate samples from the data distribution are then obtained byestimating the time-reversal of this diffusion using score matching ideas. Wefollow here a similar strategy to sample from unnormalized probabilitydensities and compute their normalizing constants. However, the time-reverseddiffusion is here simulated by using an original iterative particle schemerelying on a novel score matching loss. Contrary to standard denoisingdiffusion models, the resulting Particle Denoising Diffusion Sampler (PDDS)provides asymptotically consistent estimates under mild assumptions. Wedemonstrate PDDS on multimodal and high dimensional sampling tasks.