HIR-Diff is an unsupervised hyperspectral image (HSI) restoration framework that leverages an improved diffusion model to recover clean HSIs from degraded observations. The method assumes that HSIs can be decomposed into a reduced image and a coefficient matrix, both of which are estimated separately. The reduced image, which has a low spectral dimension, is restored using an improved diffusion model with a new guidance function that incorporates total variation (TV) prior to ensure accurate sampling. The coefficient matrix is pre-estimated using singular value decomposition (SVD) and rank-revealing QR (RRQR) factorization, which helps in determining the band indices for the reduced image. A novel exponential noise schedule is introduced to accelerate the diffusion process, achieving about 5× speedup in denoising with minimal performance loss. The framework is validated on various HSI restoration tasks, including denoising, super-resolution, and inpainting, demonstrating superior performance and efficiency compared to existing methods. The method's effectiveness is attributed to its ability to capture complex image characteristics and its efficient use of prior knowledge, making it a robust solution for HSI restoration.HIR-Diff is an unsupervised hyperspectral image (HSI) restoration framework that leverages an improved diffusion model to recover clean HSIs from degraded observations. The method assumes that HSIs can be decomposed into a reduced image and a coefficient matrix, both of which are estimated separately. The reduced image, which has a low spectral dimension, is restored using an improved diffusion model with a new guidance function that incorporates total variation (TV) prior to ensure accurate sampling. The coefficient matrix is pre-estimated using singular value decomposition (SVD) and rank-revealing QR (RRQR) factorization, which helps in determining the band indices for the reduced image. A novel exponential noise schedule is introduced to accelerate the diffusion process, achieving about 5× speedup in denoising with minimal performance loss. The framework is validated on various HSI restoration tasks, including denoising, super-resolution, and inpainting, demonstrating superior performance and efficiency compared to existing methods. The method's effectiveness is attributed to its ability to capture complex image characteristics and its efficient use of prior knowledge, making it a robust solution for HSI restoration.