  Weather forecasting remains a crucial yet challenging domain, where recently
developed models based on deep learning (DL) have approached the performance of
traditional numerical weather prediction (NWP) models. However, these DL
models, often complex and resource-intensive, face limitations in flexibility
post-training and in incorporating NWP predictions, leading to reliability
concerns due to potential unphysical predictions. In response, we introduce a
novel method that applies diffusion models (DM) for weather forecasting. In
particular, our method can achieve both direct and iterative forecasting with
the same modeling framework. Our model is not only capable of generating
forecasts independently but also uniquely allows for the integration of NWP
predictions, even with varying lead times, during its sampling process. The
flexibility and controllability of our model empowers a more trustworthy DL
system for the general weather community. Additionally, incorporating
persistence and climatology data further enhances our model's long-term
forecasting stability. Our empirical findings demonstrate the feasibility and
generalizability of this approach, suggesting a promising direction for future,
more sophisticated diffusion models without the need for retraining.
