With the emergence of Transformers and Vision-Language Models (VLMs) such as CLIP, large pre-trained models have become a common strategy to enhance performance in Continual Learning scenarios. This led to the development of numerous prompting strategies to effectively fine-tune transformer-based models without succumbing to catastrophic forgetting. However, these methods struggle to specialize the model on domains significantly deviating from the pre-training and preserving its zero-shot capabilities. In this work, we propose Continual Generative training for Incremental prompt-Learning, a novel approach to mitigate forgetting while adapting a VLM, which exploits generative replay to align prompts to tasks. We also introduce a new metric to evaluate zero-shot capabilities within CL benchmarks. Through extensive experiments on different domains, we demonstrate the effectiveness of our framework in adapting to new tasks while improving zero-shot capabilities. Further analysis reveals that our approach can bridge the gap with joint prompt tuning. The codebase is available at https://github.com/aimagelab/mammoth.