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Paper · arXiv

Foundations of Schrödinger Bridges for Generative Modeling

At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in probability space. Schrödinger bridges provide a unifying principle underlying these approaches, framing the problem as determining an optimal stochastic bridge between marginal distribution constraints with minimal-entropy deviations from a pre-defined reference process. This guide develops the mathematical foundations of the Schrödinger bridge problem, drawing on optimal transport, stochastic control, and path-space optimization, and focuses on its dy...

AuthorsSophia Tang
Primary categorycs.LG
Published19 March 2026
Last updated at source19 March 2026
cs.LGcs.AI
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