Abstract

In this first reading group of the year, we will be giving an introduction to the framework of stochastic interpolants and showing their connection to flow matching and diffusion. Stochastic interpolants enables the use of a broad class of continuous-time stochastic processes to bridge any two probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable. The time-dependent density function of the interpolant satisfies a transport equation as well as a family of forward and backward Fokker-Planck equations with a tunable diffusion coefficient. This leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise.

In the first part of the tutorial we will have a look at the theory behind stochastic interpolants. In the last part of the tutorial, we will describe an application of the stochastic interpolants framework to design a new sampling based method that seems competitive with state of the art techniques like parallel tempering.

Reading material (not necessary to read before the session):

• Building Normalizing Flows with Stochastic Interpolants Michael S. Albergo, Eric Vanden-Eijnden https://arxiv.org/abs/2209.15571

• Stochastic Interpolants: A Unifying Framework for Flows and Diffusions Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden https://arxiv.org/abs/2303.08797

• Flow Matching for Generative Modeling Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, Matt Le https://arxiv.org/abs/2210.02747