New tutorial paper on the “Foundations of Schrödinger Bridges for Generative Modeling” is out on arXiv! 🧩 📖 arXiv: arxiv.org/abs/2603.18992 🔮 Project Website: sophtang.github.io/foundations-of… With 220 pages and 24 figures, this guide builds the theoretical foundations of Schrödinger bridges from the ground up, unifying the broad field of generative modeling with a single guiding principle: construct an optimal stochastic bridge between distributions while minimizing deviation from a reference process. The rapid progress in generative modeling has made the field increasingly difficult to navigate from a foundational perspective, which motivated me to develop a resource that builds the core concepts needed to understand and contribute to new advances. This guide contains intuitive explanations and step-by-step proofs covering: 🧩 The dynamic Schrödinger bridge formulation, lifting optimal transport to continuous-time stochastic processes between distributions, with direct connections to diffusion models, score-based methods, and flow matching. 🧩 A comprehensive toolkit for constructing Schrödinger bridges from first principles, describing stochastic optimal control, forward–backward SDEs, Doob’s h-transform, and Markov and reciprocal projections. 🧩 Extensions to complex and real-world problem settings, including the multi-marginal, unbalanced, discrete SB problems, highlighting the flexibility of the Schrödinger bridge framework in describing complex dynamical systems. 🧩 Practical, scalable algorithms for training and inference of dynamic Schrödinger bridges across modern generative modeling tasks. More details in the thread 👇🏻
