Diffusion models have achieved remarkable success in generating high-quality images thanks to their novel training procedures applied to unprecedented amounts of data. However, training a diffusion model from scratch is computationally expensive. This highlights the need to investigate the possibility of training these models iteratively, reusing computation while the data distribution changes. In this study, we take the first step in this direction and evaluate the continual learning (CL) properties of diffusion models. We begin by benchmarking the most common CL methods applied to Denoising Diffusion Probabilistic Models (DDPMs), where we note the strong performance of the experience replay with the reduced rehearsal coefficient. Furthermore, we provide insights into the dynamics of forgetting, which exhibit diverse behavior across diffusion timesteps. We also uncover certain pitfalls of using the bits-per-dimension metric for evaluating CL.