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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.18992 |
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| _version_ | 1866915875520512000 |
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| author | Tang, Sophia |
| author_facet | Tang, Sophia |
| contents | 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 dynamic formulation with direct connections to modern generative modeling. We build a comprehensive toolkit for constructing Schrödinger bridges from first principles, and show how these constructions give rise to generalized and task-specific computational methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18992 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Foundations of Schrödinger Bridges for Generative Modeling Tang, Sophia Machine Learning Artificial Intelligence 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 dynamic formulation with direct connections to modern generative modeling. We build a comprehensive toolkit for constructing Schrödinger bridges from first principles, and show how these constructions give rise to generalized and task-specific computational methods. |
| title | Foundations of Schrödinger Bridges for Generative Modeling |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2603.18992 |