  Diffusion models have recently received a surge of interest due to their
impressive performance for image restoration, especially in terms of noise
robustness. However, existing diffusion-based methods are trained on a large
amount of training data and perform very well in-distribution, but can be quite
susceptible to distribution shift. This is especially inappropriate for
data-starved hyperspectral image (HSI) restoration. To tackle this problem,
this work puts forth a self-supervised diffusion model for HSI restoration,
namely Denoising Diffusion Spatio-Spectral Model (\texttt{DDS2M}), which works
by inferring the parameters of the proposed Variational Spatio-Spectral Module
(VS2M) during the reverse diffusion process, solely using the degraded HSI
without any extra training data. In VS2M, a variational inference-based loss
function is customized to enable the untrained spatial and spectral networks to
learn the posterior distribution, which serves as the transitions of the
sampling chain to help reverse the diffusion process. Benefiting from its
self-supervised nature and the diffusion process, \texttt{DDS2M} enjoys
stronger generalization ability to various HSIs compared to existing
diffusion-based methods and superior robustness to noise compared to existing
HSI restoration methods. Extensive experiments on HSI denoising, noisy HSI
completion and super-resolution on a variety of HSIs demonstrate
\texttt{DDS2M}'s superiority over the existing task-specific state-of-the-arts.
