Precipitation forecasting at fine spatiotemporal resolution is essential for refined meteorological services, yet high-resolution data remain costly to obtain and operational model outputs (e.g., the Fuxi model at 0.25°) are too coarse to resolve small- and medium-scale precipitation structures. To address this gap, this paper proposes a precipitation forecast downscaling method based on a Correlation Diffusion Network (Diffusion-U-Net) that converts low-resolution Fuxi precipitation forecasts into high-resolution fields. The method combines the probabilistic generation capability of diffusion models with the multi-scale feature extraction advantages of U-Net, and introduces a correlation module with a channel-spatial dual attention mechanism to capture the spatiotemporal correlation features of precipitation fields. Evaluated on 2020–2023 Fuxi forecasts over North China, the proposed method outperforms traditional interpolation and deep learning baselines: it achieves a structural similarity index (SSIM) of 0.81 and a heavy-precipitation critical success index (CSI) of 0.72, and reduces the heavy-precipitation intensity bias by 6% relative to vanilla U-Net. The method restores small- and medium-scale precipitation details more accurately and provides technical support for refined meteorological forecasting.