  Diffusion models are powerful generative models that simulate the reverse of
diffusion processes using score functions to synthesize data from noise. The
sampling process of diffusion models can be interpreted as solving the reverse
stochastic differential equation (SDE) or the ordinary differential equation
(ODE) of the diffusion process, which often requires up to thousands of
discretization steps to generate a single image. This has sparked a great
interest in developing efficient integration techniques for reverse-S/ODEs.
Here, we propose an orthogonal approach to accelerating score-based sampling:
Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product
space of data and variance (or diffusion time). Then, a reverse-S/ODE
integrator is used to denoise the MCMC samples. Since MCMC traverses close to
the data manifold, the computation cost of producing a clean sample for DMCMC
is much less than that of producing a clean sample from noise. To verify the
proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of
DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in
this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably,
combined with integrators of Karras et al. (2022) and pre-trained score models
of Song et al. (2021b), DLG achieves SOTA results. In the limited number of
score function evaluation (NFE) settings on CIFAR10, we have $3.86$ FID with
$\approx 10$ NFE and $2.63$ FID with $\approx 20$ NFE. On CelebA-HQ-256, we
have $6.99$ FID with $\approx 160$ NFE, which beats the current best record of
Kim et al. (2022) among score-based models, $7.16$ FID with $4000$ NFE. Code:
https://github.com/1202kbs/DMCMC
