This webpage will serve as a home base for the exposition and consolidation of concepts related to the stochastic interpolant method for generative modeling.

Stochastic interpolants are a methodological tool that make possible the learning of maps – either deterministic or stochastic – connecting probability distributions. This results in generative models that follow either a deterministic flow (aka a continuous-time normalizing flows) or a diffusion (e.g. a generalization of the score-based diffusion), with tunable levels of stochsaticity. In this page, we will detail the foundations of the concept, along with various additional perspectives on it related to optimal transport and Schödinger bridges, data-dependent couplings, and multimarginal extensions of the method, for which we consider generalized transport among $K$ probability distributions. For a thorough treatment of the various interesting and related work, see the following papers:

1. Building Normalizing Flows with Stochastic Interpolants (2022)

2. Stochastic Interpolants: A unifying framework for flows and diffusions (2023)

3. Stochastic interpolants with data-dependent couplings (2023)

4. Multimarginal generative modeling with stochastic interpolants (2023)

Here are the contacts for the authors contributing to these works!