Self-Supervised Variational Diffusion with Temporal Tucker Modeling for Hyperspectral Image Restoration

Hyperspectral image (HSI) restoration aims to recover spatial structures and spectrally faithful signatures from measurements affected by noise, missing observations, and spatial degradation. Existing supervised methods often generalize poorly across sensors and corruption distributions, while model-based approaches rely heavily on manually designed priors with limited expressive ability. Diffusion-based HSI restoration provides a promising alternative, but existing methods remain limited in modeling complex hyperspectral corruption and in fully exploiting the regularization imposed by diffusion sampling and HSI-specific priors. To address these limitations, we propose VITTA, a self-supervised $\underline{v}$ariational d$\underline{i}$ffusion framework with $\underline{t}$emporal $\underline{T}$ucker modeling for HSI restor$\underline{a}$tion. Specifically, VITTA couples a likelihood step and a prior step within the reverse diffusion process. In the likelihood step, a two-factor probabilistic model characterizes complex HSI corruption, and the inferred non-Gaussian uncertainty is projected into Gaussian observation channels to provide reliability-aware measurement conditioning. Complementarily, the prior step employs a Temporal Tucker Prior Module to estimate the clean endpoint under joint spatial, spectral, and reverse-step regularization. The resulting likelihood and prior information are then integrated through reliability-guided conditional diffusion sampling to progressively restore the HSI. Theoretically, we establish approximation guarantees and recursive error bounds, verifying the feasibility of the proposed progressive recovery process. Extensive experiments demonstrate that our proposed method outperforms state-of-the-art methods on various tasks including HSI denoising, band completion and pansharpening.