Foundations of Schrödinger Bridges for Generative Modeling

This paper explains Schrödinger bridges, a mathematical framework that unifies popular AI generative models like diffusion models and flow matching. The core idea is finding the optimal way to transform a simple distribution into a complex one while minimizing entropy deviation, which the paper develops from first principles using tools from optimal transport and stochastic control. The work provides both theoretical foundations and practical methods for building these bridges, connecting abstract mathematics to modern generative AI techniques.