Explore optimal transport techniques for machine learning in this 42-minute conference talk by Gabriel Peyre from Ecole Normale Superieure. Delve into probability distributions in data sciences, focusing on Kantorovitch's formulation, optimal transport distances, and entropic regularization. Examine Sinkhorn divergences and sample complexity before transitioning to density fitting and generative models. Compare deep discriminative and generative models, discussing training architectures and automatic differentiation. Analyze examples of image generation and generative adversarial networks. Conclude by considering open problems in the field. This talk, part of the Isaac Newton Institute's workshop on "Approximation, sampling and compression in data science," bridges various mathematical aspects of data science, fostering collaboration among researchers in computational statistics, machine learning, optimization, information theory, and learning theory.