SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations

Grigory Bartosh, Dmitry Vetrov, Christian A. Naesseth
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:3054-3070, 2025.

Abstract

The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation through approximate SDE solutions, which limit scalability. In this work, we propose SDE Matching, a new simulation-free method for training Latent SDEs. Inspired by modern Score- and Flow Matching algorithms for learning generative dynamics, we extend these ideas to the domain of stochastic dynamics for time series modeling, eliminating the need for costly numerical simulations. Our results demonstrate that SDE Matching achieves performance comparable to adjoint sensitivity methods while drastically reducing computational complexity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-bartosh25a, title = {{SDE} Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations}, author = {Bartosh, Grigory and Vetrov, Dmitry and Naesseth, Christian A.}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {3054--3070}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/bartosh25a/bartosh25a.pdf}, url = {https://proceedings.mlr.press/v267/bartosh25a.html}, abstract = {The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation through approximate SDE solutions, which limit scalability. In this work, we propose SDE Matching, a new simulation-free method for training Latent SDEs. Inspired by modern Score- and Flow Matching algorithms for learning generative dynamics, we extend these ideas to the domain of stochastic dynamics for time series modeling, eliminating the need for costly numerical simulations. Our results demonstrate that SDE Matching achieves performance comparable to adjoint sensitivity methods while drastically reducing computational complexity.} }
Endnote
%0 Conference Paper %T SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations %A Grigory Bartosh %A Dmitry Vetrov %A Christian A. Naesseth %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-bartosh25a %I PMLR %P 3054--3070 %U https://proceedings.mlr.press/v267/bartosh25a.html %V 267 %X The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation through approximate SDE solutions, which limit scalability. In this work, we propose SDE Matching, a new simulation-free method for training Latent SDEs. Inspired by modern Score- and Flow Matching algorithms for learning generative dynamics, we extend these ideas to the domain of stochastic dynamics for time series modeling, eliminating the need for costly numerical simulations. Our results demonstrate that SDE Matching achieves performance comparable to adjoint sensitivity methods while drastically reducing computational complexity.
APA
Bartosh, G., Vetrov, D. & Naesseth, C.A.. (2025). SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:3054-3070 Available from https://proceedings.mlr.press/v267/bartosh25a.html.

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