Distributional Diffusion Models with Scoring Rules
Journal:
arXiv
Published Date:
Feb 4, 2025
Abstract
Diffusion models generate high-quality synthetic data. They operate by
defining a continuous-time forward process which gradually adds Gaussian noise
to data until fully corrupted. The corresponding reverse process progressively
"denoises" a Gaussian sample into a sample from the data distribution. However,
generating high-quality outputs requires many discretization steps to obtain a
faithful approximation of the reverse process. This is expensive and has
motivated the development of many acceleration methods. We propose to
accomplish sample generation by learning the posterior {\em distribution} of
clean data samples given their noisy versions, instead of only the mean of this
distribution. This allows us to sample from the probability transitions of the
reverse process on a coarse time scale, significantly accelerating inference
with minimal degradation of the quality of the output. This is accomplished by
replacing the standard regression loss used to estimate conditional means with
a scoring rule. We validate our method on image and robot trajectory
generation, where we consistently outperform standard diffusion models at few
discretization steps.
