Nowcasting is an observation-based method that uses the current state of the atmosphere to forecast future weather conditions over several hours. Recent studies have shown the promising potential of using deep learning models for precipitation nowcasting. In this paper, novel deep generative models are proposed for precipitation nowcasting. These models are equipped with extreme-value losses to more reliably predict extreme precipitation events. The proposed deep generative model contains a Vector Quantization Generative Adversarial Network and a Transformer ("VQGAN + Transformer"). For enhanced modeling and forecasting of extreme events, Extreme Value Loss (EVL) is incorporated in the autore-gressive Transformer. The numerical results show that the proposed model achieves comparable performance with the state-of-the-art conventional nowcasting method PySTEPS for predicting nominal values. By incorporating an EVL, the proposed model yields more accurate nowcasting of extreme precipitation.