  Existing image restoration methods mostly leverage the posterior distribution
of natural images. However, they often assume known degradation and also
require supervised training, which restricts their adaptation to complex real
applications. In this work, we propose the Generative Diffusion Prior (GDP) to
effectively model the posterior distributions in an unsupervised sampling
manner. GDP utilizes a pre-train denoising diffusion generative model (DDPM)
for solving linear inverse, non-linear, or blind problems. Specifically, GDP
systematically explores a protocol of conditional guidance, which is verified
more practical than the commonly used guidance way. Furthermore, GDP is
strength at optimizing the parameters of degradation model during the denoising
process, achieving blind image restoration. Besides, we devise hierarchical
guidance and patch-based methods, enabling the GDP to generate images of
arbitrary resolutions. Experimentally, we demonstrate GDP's versatility on
several image datasets for linear problems, such as super-resolution,
deblurring, inpainting, and colorization, as well as non-linear and blind
issues, such as low-light enhancement and HDR image recovery. GDP outperforms
the current leading unsupervised methods on the diverse benchmarks in
reconstruction quality and perceptual quality. Moreover, GDP also generalizes
well for natural images or synthesized images with arbitrary sizes from various
tasks out of the distribution of the ImageNet training set.
