Diffusion models have recently gained significant attention in probabilistic machine learning due to their theoretical properties and impressive applications in generative AI, including Stable Diffusion and DALL-E. This talk will provide a brief introduction to the theory of score-based diffusion models in Euclidean space. It will also present recent findings on score-based generative modeling in infinite-dimensional spaces, based on the time reversal theory of diffusion processes in Hilbert space.