This is a placeholder notebook on learning Schrödinger bridges, which formalise the stochastic bridge processes and have some connections to optimal transport.
I am mostly interested in these as a means to condition neural denoising diffusion models.
1 References
Albergo, Boffi, and Vanden-Eijnden. 2023. “Stochastic Interpolants: A Unifying Framework for Flows and Diffusions.”
Brekelmans, and Neklyudov. 2023. “On Schrödinger Bridge Matching and Expectation Maximization.”
De Bortoli, Thornton, Heng, et al. 2021. “Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling.” In Proceedings of the 35th International Conference on Neural Information Processing Systems. NIPS ’21.
Gottwald, Li, Marzouk, et al. 2024. “Stable Generative Modeling Using Schrödinger Bridges.”
Gottwald, and Reich. 2024. “Localized Schrödinger Bridge Sampler.”
Heng, De Bortoli, Doucet, et al. 2022. “Simulating Diffusion Bridges with Score Matching.”
Kieu, Do, Nguyen, et al. 2025. “Bidirectional Diffusion Bridge Models.”
Malory, and Sherlock. 2016. “Residual-Bridge Constructs for Conditioned Diffusions.”
Nguyen, Do, Kieu, et al. 2025. “H-Edit: Effective and Flexible Diffusion-Based Editing via Doob’s h-Transform.” In.
Shi, Bortoli, Deligiannidis, et al. 2022. “Conditional Simulation Using Diffusion Schrödinger Bridges.”