In this talk, I will discuss connections between control problems that arise in nonequilibrium statistical physics and generative models to illustrate how tools built for low dissipation control and rare event sampling can be leveraged to improve sample efficiency in flow-based generative models. Employing these notions, I will outline a strategy for parameterizing discrete diffusion models using tensor networks, which improves MCMC in some simple models from statistical mechanics. Going beyond this approach, I will discuss "mixed-resolution" discrete and continuous models we have been developing and how to build statistically controlled sampling schemes for these models.