Precipitation nowcasting is a crucial element in current weather service systems. Data-driven methods have proven highly advantageous, due to their flexibility in utilizing detailed initial hydrometeor observations, and their capability to approximate meteorological dynamics effectively given sufficient training data. However, current data-driven methods often encounter severe approximation/optimization errors, rendering their predictions and associated uncertainty estimates unreliable. Here we develop a probabilistic diffusion model-based precipitation nowcasting methodology, overcoming the notorious blurriness and mode collapse issues in existing practices. Our approach results in a 3.7% improvement in continuous ranked probability score compared to state-of-the-art generative adversarial model-based method. Critically, we significantly enhance the reliability of forecast uncertainty estimates, evidenced in a 68% gain of spread-skill ratio skill. As a result, our approach provides more reliable probabilistic precipitation nowcasting, showing the potential to better support weather-related decision makings.