Mathematics Colloquium
Nizar Touzi
NYU
Title: Bridging Schroedinger and Bass for generative diffusion modeling
Date: Friday, February 20th
Place and Time: Love 101, 3:05-3:55 pm
Abstract. Generative models aim to approximate an unknown probability distribution mu on Rd using a finite sample of independent draws from mu. Motivated by variance-preserving score-based diffusion models, we introduce a new diffusion-based transport plan on path space that is optimal with respect to a criterion combining entropy minimization and stabilization of the quadratic variation. The resulting transport plan can be interpreted as an interpolation between the Schroedinger bridge and the Bass solution from martingale optimal transport. The proposed method has a computational complexity comparable to that of state-of-the-art approaches, while yielding a significant improvement in generation quality.