Precipitation nowcasting is a vital spatio-temporal prediction task for meteorological applications but faces challenges due to the chaotic property of precipitation systems. Existing methods predominantly rely on single-source radar data to build either deterministic or probabilistic models for extrapolation. However, the single deterministic model suffers from blurring due to MSE convergence. The single probabilistic model, typically represented by diffusion models, can generate fine details but suffers from spurious artifacts that compromise accuracy and computational inefficiency. To address these challenges, this paper proposes a novel coarse-to-fine Vision Mamba Unet and residual Diffusion (VMU-Diff) based precipitation nowcasting framework. It realizes precipitation nowcasting through a two-stage process, i.e., a deterministic model-based coarse stage to predict global motion trends and a probabilistic model-based fine stage to generate fine prediction details. In the coarse prediction stage, rather than single-source radar data, both radar and multi-band satellite data are taken as input. A spatial-temporal attention block and several Vision mamba state-space blocks realize multi-source data fusion, and predict the future echo global dynamics. The fine-grained stage is realized by a spatio-temporal refine generator based on residual conditional diffusion models. It first obtains spatio-temporal residual features based on coarse prediction and ground truth, and further reconstructs the residual via conditional Mamba state-space module. Experiments on Jiangsu SWAN datasets demonstrate the improvements of our method over state-of-the-art methods, particularly in short-term forecasts.