Generative models are used as an alternative data augmentation technique to alleviate the data scarcity problem faced in the medical imaging field. Diffusion models have gathered special attention due to their innovative generation approach, the high quality of the generated images and their relatively less complex training process compared with Generative Adversarial Networks. Still, the implementation of such models in the medical domain remains at early stages. In this work, we propose exploring the use of diffusion models for the generation of high quality full-field digital mammograms using state-of-the-art conditional diffusion pipelines. Additionally, we propose using stable diffusion models for the inpainting of synthetic lesions on healthy mammograms. We introduce MAM-E, a pipeline of generative models for high quality mammography synthesis controlled by a text prompt and capable of generating synthetic lesions on specific regions of the breast. Finally, we provide quantitative and qualitative assessment of the generated images and easy-to-use graphical user interfaces for mammography synthesis.