Hyperspectral image (HSI) analysis plays a critical role in remote sensing, agriculture, and environmental monitoring. However, traditional methods often struggle to handle the high dimensionality, spectral redundancy, and noise inherent in HSI data, limiting their accuracy and scalability. Recently, diffusion models including denoising diffusion probabilistic models and other generative frameworks based on stochastic differential equations have shown strong potential in capturing complex spectral spatial structures and generating high fidelity HSI data. These models offer effective solutions for tasks such as noise supression, data augmentation, classification, and anomaly detection. This review presents a systematic summary of recent advances in diffusion models for HSI processing. We categorize existing methods, highlight their strengths in handling high dimensional data, and compare their performance with conventional approaches. Special attention is given to critical applications such as change detection and post disaster anomaly identification. The review also discusses current limitations, such as computational cost and training stability, and outlines potential research directions. Our main contributions can be summarized as follows: we provide a systematic taxonomy of diffusion based HSI methods, examine their applications across major remote sensing tasks, and offer perspectives on potential directions for future research. With these efforts, this review seeks to support the community in harnessing deep learning models to achieve more effective and efficient hyperspectral image analysis.