  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 Schr\"odinger bridges and finally demonstrate
DDS experimentally on a variety of challenging sampling tasks.
