Denoising Diffusion Samplers
This provides a novel method for Monte Carlo sampling in domains like statistics and machine learning, though it builds incrementally on existing diffusion model ideas.
The paper tackles the problem of sampling from unnormalized probability density functions and estimating their normalizing constants by adapting denoising diffusion models, demonstrating DDS experimentally on challenging sampling tasks with theoretical guarantees.
Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution. Samples from the generative model are then obtained by simulating an approximation of the time-reversal of this diffusion initialized by Gaussian samples. Practically, the intractable score terms appearing in the time-reversed process are approximated using score matching techniques. We explore here a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. We consider a process where the target density diffuses towards a Gaussian. Denoising Diffusion Samplers (DDS) are obtained by approximating the corresponding time-reversal. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling. Existing theoretical results from denoising diffusion models also provide theoretical guarantees for DDS. We discuss the connections between DDS, optimal control and Schrödinger bridges and finally demonstrate DDS experimentally on a variety of challenging sampling tasks.