Diffusion models showcase strong capabilities in image synthesis, being used in many computer vision tasks with great success. To this end, we propose to explore a new use case, namely to copy black-box classification models without having access to the original training data, the architecture, and the weights of the model, i.e. the model is only exposed through an inference API. More specifically, we can only observe the (soft or hard) labels for some image samples passed as input to the model. Furthermore, we consider an additional constraint limiting the number of model calls, mostly focusing our research on few-call model stealing. In order to solve the model extraction task given the applied restrictions, we propose the following framework. As training data, we create a synthetic data set (called proxy data set) by leveraging the ability of diffusion models to generate realistic and diverse images. Given a maximum number of allowed API calls, we pass the respective number of samples through the black-box model to collect labels. Finally, we distill the knowledge of the black-box teacher (attacked model) into a student model (copy of the attacked model), harnessing both labeled and unlabeled data generated by the diffusion model. We employ a novel active self-paced learning framework to make the most of the proxy data during distillation. Our empirical results on three data sets confirm the superiority of our framework over four state-of-the-art methods in the few-call model extraction scenario. We release our code for free non-commercial use at https://github.com/vladhondru25/model-stealing.