The trade-off between imaging efficiency and imaging quality has always been encountered by Fourier single-pixel imaging (FSPI). To achieve high-resolution imaging, the increase in the number of measurements is necessitated, resulting in a reduction of imaging efficiency. Here, a novel high-quality reconstruction method for FSPI imaging via diffusion model was proposed. A score-based diffusion model is designed to learn prior information of the data distribution. The real-sampled low-frequency Fourier spectrum of the target is employed as a consistency term to iteratively constrain the model in conjunction with the learned prior information, achieving high-resolution reconstruction at extremely low sampling rates. The performance of the proposed method is evaluated by simulations and experiments. The results show that the proposed method has achieved superior quality compared with the traditional FSPI method and the U-Net method. Especially at the extremely low sampling rate (e.g., 1%), an approximately 241% improvement in edge intensity-based score was achieved by the proposed method for the coin experiment, compared with the traditional FSPI method. The method has the potential to achieve high-resolution imaging without compromising imaging speed, which will further expanding the application scope of FSPI in practical scenarios.