HIR-Diff is an unsupervised hyperspectral image (HSI) restoration framework that leverages improved diffusion models to recover clean HSIs from degraded observations. The method restores HSIs by decomposing them into two low-rank components: a reduced image with a low spectral dimension and a coefficient matrix. The reduced image is inferred using an improved diffusion model with a new guidance function incorporating total variation (TV) prior, while the coefficient matrix is pre-estimated via singular value decomposition (SVD) and rank-revealing QR (RRQR) factorization. A novel exponential noise schedule is introduced to accelerate the restoration process, achieving approximately 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 leverage prior knowledge of low-rank and TV properties, enabling robust and efficient restoration. The proposed approach is a generalizable HSI restoration framework that outperforms state-of-the-art methods in both performance and speed.HIR-Diff is an unsupervised hyperspectral image (HSI) restoration framework that leverages improved diffusion models to recover clean HSIs from degraded observations. The method restores HSIs by decomposing them into two low-rank components: a reduced image with a low spectral dimension and a coefficient matrix. The reduced image is inferred using an improved diffusion model with a new guidance function incorporating total variation (TV) prior, while the coefficient matrix is pre-estimated via singular value decomposition (SVD) and rank-revealing QR (RRQR) factorization. A novel exponential noise schedule is introduced to accelerate the restoration process, achieving approximately 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 leverage prior knowledge of low-rank and TV properties, enabling robust and efficient restoration. The proposed approach is a generalizable HSI restoration framework that outperforms state-of-the-art methods in both performance and speed.