Generative AI is one of the most promising avenues towards gaining a deeper understanding of the vast amount of data available in our modern world. A generative model aims to learn the underlying patterns of a dataset, resulting in the ability to synthesize new and realistic data examples. Denoising diffusion probabilistic models are the current state-of-the art generative deep learning approaches behind some of the most striking examples of image (DALL-E) and text (GENIE) generation. Notably, diffusion models have recently been used to generate realistic protein sequences and structures, proving to be a powerhouse in the life-sciences domain. In this talk we introduce the theoretical foundation and formulation of diffusion models, then discuss their use and application in protein design problems.