Particle Denoising Diffusion Sampler
This provides a method for sampling and normalization in probabilistic modeling, with potential applications in statistics and machine learning, though it appears incremental as it builds on existing denoising diffusion models.
The paper tackled the problem of sampling from unnormalized probability densities and computing their normalizing constants by introducing the Particle Denoising Diffusion Sampler (PDDS), which uses an iterative particle scheme with a novel score matching loss to achieve asymptotically consistent estimates, as demonstrated on multimodal and high-dimensional tasks.
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.