Fusion-based hyperspectral image (HSI) super-resolution aims to produce a high-spatial-resolution HSI by fusing a low-spatial-resolution HSI and a high-spatial-resolution multispectral image. Such a HSI super-resolution process can be modeled as an inverse problem, where the prior knowledge is essential for obtaining the desired solution. Motivated by the success of diffusion models, we propose a novel spectral diffusion prior for fusion-based HSI super-resolution. Specifically, we first investigate the spectrum generation problem and design a spectral diffusion model to model the spectral data distribution. Then, in the framework of maximum a posteriori, we keep the transition information between every two neighboring states during the reverse generative process, and thereby embed the knowledge of trained spectral diffusion model into the fusion problem in the form of a regularization term. At last, we treat each generation step of the final optimization problem as its subproblem, and employ the Adam to solve these subproblems in a reverse sequence. Experimental results conducted on both synthetic and real datasets demonstrate the effectiveness of the proposed approach. The code of the proposed approach will be available on https://github.com/liuofficial/SDP.

融合基于高光谱图像（HSI）的超分辨率通过融合低空间分辨率的HSI和高空间分辨率的多光谱图像来产生高空间分辨率的HSI。本文提出了一种新颖的基于光谱扩散的先验方法来实现HSI超分辨率。在最大后验概率的框架下，通过反向生成过程保留每两个相邻状态之间的转移信息，并将训练好的光谱扩散模型的知识嵌入到融合问题中作为正则化项。最后，将最终优化问题的每个生成步骤视为其子问题，并使用Adam算法以反向顺序解决这些子问题。在合成和真实数据集上进行的实验结果证明了所提方法的有效性。所提方法的代码将在此https网址上提供。

高光谱图像超分辨率的光谱扩散先验