Personalized text-to-image diffusion models have grown popular for their ability to efficiently acquire a new concept from user-defined text descriptions and a few images. However, in the real world, a user may wish to personalize a model on multiple concepts but one at a time, with no access to the data from previous concepts due to storage/privacy concerns. When faced with this continual learning (CL) setup, most personalization methods fail to find a balance between acquiring new concepts and retaining previous ones -- a challenge that continual personalization (CP) aims to solve. Inspired by the successful CL methods that rely on class-specific information for regularization, we resort to the inherent class-conditioned density estimates, also known as diffusion classifier (DC) scores, for CP of text-to-image diffusion models. Namely, we propose using DC scores for regularizing the parameter-space and function-space of text-to-image diffusion models.Using several diverse evaluation setups, datasets, and metrics, we show that our proposed regularization-based CP methods outperform the state-of-the-art C-LoRA, and other baselines. Finally, by operating in the replay-free CL setup and on low-rank adapters, our method incurs zero storage and parameter overhead, respectively, over the state-of-the-art.