Aligned Diffusion Schrödinger Bridges
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916225299251200 |
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| author | Somnath, Vignesh Ram Pariset, Matteo Hsieh, Ya-Ping Martinez, Maria Rodriguez Krause, Andreas Bunne, Charlotte |
| author_facet | Somnath, Vignesh Ram Pariset, Matteo Hsieh, Ya-Ping Martinez, Maria Rodriguez Krause, Andreas Bunne, Charlotte |
| contents | Diffusion Schrödinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms for solving DSBs have so far failed to utilize the structure of aligned data, which naturally arises in many biological phenomena. In this paper, we propose a novel algorithmic framework that, for the first time, solves DSBs while respecting the data alignment. Our approach hinges on a combination of two decades-old ideas: The classical Schrödinger bridge theory and Doob's $h$-transform. Compared to prior methods, our approach leads to a simpler training procedure with lower variance, which we further augment with principled regularization schemes. This ultimately leads to sizeable improvements across experiments on synthetic and real data, including the tasks of predicting conformational changes in proteins and temporal evolution of cellular differentiation processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11419 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Aligned Diffusion Schrödinger Bridges Somnath, Vignesh Ram Pariset, Matteo Hsieh, Ya-Ping Martinez, Maria Rodriguez Krause, Andreas Bunne, Charlotte Machine Learning Quantitative Methods Diffusion Schrödinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms for solving DSBs have so far failed to utilize the structure of aligned data, which naturally arises in many biological phenomena. In this paper, we propose a novel algorithmic framework that, for the first time, solves DSBs while respecting the data alignment. Our approach hinges on a combination of two decades-old ideas: The classical Schrödinger bridge theory and Doob's $h$-transform. Compared to prior methods, our approach leads to a simpler training procedure with lower variance, which we further augment with principled regularization schemes. This ultimately leads to sizeable improvements across experiments on synthetic and real data, including the tasks of predicting conformational changes in proteins and temporal evolution of cellular differentiation processes. |
| title | Aligned Diffusion Schrödinger Bridges |
| topic | Machine Learning Quantitative Methods |
| url | https://arxiv.org/abs/2302.11419 |