Diffusion models are powerful generative models that achieve state-of-the-art performance in tasks such as image synthesis. However, training them demands substantial amounts of data and computational resources. Continual learning would allow for incrementally learning new tasks and accumulating knowledge, thus reusing already trained models would be possible. One potentially suitable approach is generative replay, where a copy of a generative model trained on previous tasks produces synthetic data that are interleaved with data from the current task. However, standard generative replay applied to diffusion models results in a catastrophic loss in denoising capabilities. In this paper, we propose generative distillation, an approach that distils the entire reverse process of a diffusion model. We demonstrate that our approach significantly improves the continual learning performance of generative replay with only a moderate increase in the computational costs.