Variational and stochastic flows are now ubiquitous in machine learning and generative modeling. Indeed, many such models can be interpreted as flows from a latent distribution to the sample
distribution, and training corresponds to finding the right flow vector field. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient, and Hamiltonian flows. Recently, mean-field control and mean-field games offer general optimal control variational problems on the learning problem. How do these tools lead us to a better understanding and further development of machine learning and generative models?