  Hyperspectral image (HSI) restoration aims at recovering clean images from
degraded observations and plays a vital role in downstream tasks. Existing
model-based methods have limitations in accurately modeling the complex image
characteristics with handcraft priors, and deep learning-based methods suffer
from poor generalization ability. To alleviate these issues, this paper
proposes an unsupervised HSI restoration framework with pre-trained diffusion
model (HIR-Diff), which restores the clean HSIs from the product of two
low-rank components, i.e., the reduced image and the coefficient matrix.
Specifically, the reduced image, which has a low spectral dimension, lies in
the image field and can be inferred from our improved diffusion model where a
new guidance function with total variation (TV) prior is designed to ensure
that the reduced image can be well sampled. The coefficient matrix can be
effectively pre-estimated based on singular value decomposition (SVD) and
rank-revealing QR (RRQR) factorization. Furthermore, a novel exponential noise
schedule is proposed to accelerate the restoration process (about 5$\times$
acceleration for denoising) with little performance decrease. Extensive
experimental results validate the superiority of our method in both performance
and speed on a variety of HSI restoration tasks, including HSI denoising, noisy
HSI super-resolution, and noisy HSI inpainting. The code is available at
https://github.com/LiPang/HIRDiff.
