Abstract: Flow-based generative models offer a means of sampling from complex, high-dimensional distributions. I will discuss recent work on applying these models in the context of MCMC sampling of lattice field theory distributions. Estimating observables over these (Boltzmann) distributions gives access to information about correlation functions and the spectra of quantum field theories. I will show results from flow models trained to sample the distribution for a two-dimensional scalar lattice field theory, and compare against standard simulation methods. Several developments are required to move towards lattice gauge theories, and I will discuss preliminary work in that direction.