Nicholas Boffi - Generative modeling with stochastic interpolants

Generative modeling with stochastic interpolants

Abstract: We introduce a class of generative models that unifies flows and diffusions. These models are built using a continuous-time stochastic process called a stochastic interpolant, which exactly connects two arbitrary probability densities in finite time. We show that the time-dependent density of the stochastic interpolant satisfies both a first-order transport equation and an infinite family of forward and backward Fokker-Planck equations with tunable diffusion coefficients. This viewpoint yields deterministic and stochastic generative models built dynamically from an ordinary or stochastic differential equation with an adjustable noise level. To formulate a practical algorithm, we discuss how the resulting drift functions can be characterized variationally and learned efficiently over flexible parametric classes such as neural networks. Empirically, we highlight the advantages of our formalism -- and the tradeoffs between deterministic and stochastic sampling -- through numerical examples in image generation, inverse imaging, probabilistic forecasting, and accelerated sampling.