This talk will trace the development of computational statistics (and machine learning) from the inception of Markov Chain Monte Carlo in the 1940s at Los Alamos to the current advances in generative AI (see, e.g. https://deepai.org/machine-learning-model/text2img). The story is closely connected to the analysis of diffusion processes, and we will see interactions with neighbouring fields such as PDEs, stochastic analysis and geometry.