Department of Industrial Engineering & Decision Analytics [Joint IEDA/MATH] seminar - Bridging Shrödinger and Bass for Generative Diffusion Modeling
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Generative models aim to approximate an unknown probability distribution in high dimensional space using a finite sample of independent draws. 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 Schrödinger 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.
Nizar Touzi holds a PhD from the University Paris Dauphine in January 1994, where he was appointed Assistant Professor. After a passage by University Pantheon Sorbonne, ENSAE as head of the finance and actuarial sciences lab, and Imperial College London, he served as Professor of applied mathematics and head of the financial mathematics group at Ecole Polytechnique from 2006 to 2023, where he took various responsibilities including chair of his department and head of the doctoral school in Mathematics from 2021 to 2023.
Nizar was invited to the International Congress of Mathematicians (Hyderabad 2010) as a session speaker and received the Louis Bachelier prize of the French Academy of Sciences in 2012 and the Paris Europlace prize of Best Young Researcher in Finance in 2007. He obtained many research grants, including the prestigious Advanced ERC grant. He is co-editor and associate editor in various international journals in the fields of financial mathematics, applied probability, and control theory.