  Many interesting tasks in image restoration can be cast as linear inverse
problems. A recent family of approaches for solving these problems uses
stochastic algorithms that sample from the posterior distribution of natural
images given the measurements. However, efficient solutions often require
problem-specific supervised training to model the posterior, whereas
unsupervised methods that are not problem-specific typically rely on
inefficient iterative methods. This work addresses these issues by introducing
Denoising Diffusion Restoration Models (DDRM), an efficient, unsupervised
posterior sampling method. Motivated by variational inference, DDRM takes
advantage of a pre-trained denoising diffusion generative model for solving any
linear inverse problem. We demonstrate DDRM's versatility on several image
datasets for super-resolution, deblurring, inpainting, and colorization under
various amounts of measurement noise. DDRM outperforms the current leading
unsupervised methods on the diverse ImageNet dataset in reconstruction quality,
perceptual quality, and runtime, being 5x faster than the nearest competitor.
DDRM also generalizes well for natural images out of the distribution of the
observed ImageNet training set.
