Aligned Diffusion Schrödinger Bridges

Vignesh Ram Somnath, Matteo Pariset, Ya-Ping Hsieh, Maria Rodriguez Martinez, Andreas Krause, Charlotte Bunne
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:1985-1995, 2023.

Abstract

Diffusion Schrödinger bridges (DSBs) 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-somnath23a, title = {Aligned Diffusion {S}chrödinger Bridges}, author = {Somnath, Vignesh Ram and Pariset, Matteo and Hsieh, Ya-Ping and Martinez, Maria Rodriguez and Krause, Andreas and Bunne, Charlotte}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {1985--1995}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/somnath23a/somnath23a.pdf}, url = {https://proceedings.mlr.press/v216/somnath23a.html}, abstract = {Diffusion Schrödinger bridges (DSBs) 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.} }
Endnote
%0 Conference Paper %T Aligned Diffusion Schrödinger Bridges %A Vignesh Ram Somnath %A Matteo Pariset %A Ya-Ping Hsieh %A Maria Rodriguez Martinez %A Andreas Krause %A Charlotte Bunne %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-somnath23a %I PMLR %P 1985--1995 %U https://proceedings.mlr.press/v216/somnath23a.html %V 216 %X Diffusion Schrödinger bridges (DSBs) 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.
APA
Somnath, V.R., Pariset, M., Hsieh, Y., Martinez, M.R., Krause, A. & Bunne, C.. (2023). Aligned Diffusion Schrödinger Bridges. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:1985-1995 Available from https://proceedings.mlr.press/v216/somnath23a.html.

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