Modern generative models can be viewed as dynamic transports that transform a simple source distribution into a complex target distribution.  In the stochastic setting, the Schrödinger bridge provides a classical and computationally tractable formulation: among all diffusions matching two prescribed marginal laws, it selects the one closest to Brownian motion.  However, the classical Schrödinger bridge learns a drift while keeping the volatility fixed, which is restrictive in applications where uncertainty itself is part of the signal, notably in finance.

In this talk, I will introduce the Schrödinger–Bass Bridge, a semimartingale optimal transport problem that interpolates between the Schrödinger bridge and the Bass martingale transport.  The resulting optimal dynamics learn both drift and volatility. I will describe the associated Schrödinger–Bass system, its interpretation as a Bass transport of a Schrödinger bridge, and the resulting fixed-point algorithm.  I will then discuss applications to generative modeling, first for image synthesis and then for financial time series.  In the time-series setting, the method leads to SBBTS, a sequential generative model designed to preserve temporal dependence and stochastic volatility.  Numerical experiments illustrate its ability to recover hidden Heston-type volatility and correlation structures and to improve downstream forecasting through synthetic data augmentation.

This presentation has been archived in the TTU Mediasite catalog ... 
mediacast.ttu.edu/Mediasite/Play/40e41fa08bed4e82b7561dbe488046981d