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Data-driven medium-range weather forecasting has attracted much attention in recent years. However, the forecasting accuracy at high resolution is unsatisfactory currently. Pursuing high-resolution and high-quality weather forecasting, we develop a data-driven model SwinRDM which integrates an improved version of SwinRNN with a diffusion model. SwinRDM performs predictions at 0.25-degree resolution and achieves superior forecasting accuracy to IFS (Integrated Forecast System), the state-of-the-art operational NWP model, on representative atmospheric variables including 500 hPa geopotential (Z500), 850 hPa temperature (T850), 2-m temperature (T2M), and total precipitation (TP), at lead times of up to 5 days. We propose to leverage a two-step strategy to achieve high-resolution predictions at 0.25-degree considering the trade-off between computation memory and forecasting accuracy. Recurrent predictions for future atmospheric fields are firstly performed at 1.40625-degree resolution, and then a diffusion-based super-resolution model is leveraged to recover the high spatial resolution and finer-scale atmospheric details. SwinRDM pushes forward the performance and potential of data-driven models for a large margin towards operational applications.