Bridging Schrödinger and Bass: A Unifying Framework for Generative Modeling

Professor Huyên Pham, Ecole Polytechnique, President of the Bachelier Finance Society

Bridging Schrödinger and Bass: A Unifying Framework for Generative Modeling from Images to Time Series

Recent advances in generative AI, such as diffusion models, aim to transform simple random noise into complex data like images, audio, or time series.
In this talk, I introduce a new framework that builds on this idea by learning richer stochastic dynamics directly from data. The approach combines two classical perspectives from probability theory—Schrödinger bridges and martingale transport—into a unified model called the Schrödinger–Bass bridge (SBB). Unlike standard diffusion models, this framework allows us to capture both the structure and the variability of the data, leading to more flexible and realistic generative models. I will first give an intuitive overview of the method and show how it can be used for image generation, where it enables more consistent transformations such as age progression while preserving identity. I will then present an extension to time series, called SBBTS, designed to model temporal data. Applied to financial data, SBBTS can capture key features such as stochastic volatility and generate synthetic time series that improve forecasting performance and risk-adjusted returns when used for data augmentation.