This paper addresses the problem of hyperspectral image reconstruction, which reconstructs 3D hyperspectral images (HSIs) from disturbed 2D measurements. Pointing out that existing deep learning-based methods have difficulty in accurately capturing high-frequency details, we propose a spectral spread dictionary (SDP) implicitly learned from hyperspectral images using a diffusion model. By leveraging the detail restoration ability of the diffusion model, the learned dictionary is applied to the HSI model to significantly improve its performance. In addition, to further enhance the effectiveness of the learned dictionary, a spectral dictionary injection module (SPIM) is proposed to induce the model to dynamically restore HSI details. The proposed method is evaluated on two representative HSI methods, MST and BISRNet, and the performance is improved by about 0.5 dB over the conventional networks.