Precipitation nowcasting is an important spatio-temporal prediction task to predict the radar echoes sequences based on current observations, which can serve both meteorological science and smart city applications. Due to the chaotic evolution nature of the precipitation systems, it is a very challenging problem. Previous studies address the problem either from the perspectives of deterministic modeling or probabilistic modeling. However, their predictions suffer from the blurry, high-value echoes fading away and position inaccurate issues. The root reason of these issues is that the chaotic evolutionary precipitation systems are not appropriately modeled. Inspired by the nature of the systems, we propose to decompose and model them from the perspective of global deterministic motion and local stochastic variations with residual mechanism. A unified and flexible framework that can equip any type of spatio-temporal models is proposed based on residual diffusion, which effectively tackles the shortcomings of previous methods. Extensive experimental results on four publicly available radar datasets demonstrate the effectiveness and superiority of the proposed framework, compared to state-of-the-art techniques. Our code will be made publicly available upon acceptance.