Score matching for bridges without learning time-reversals

Elizabeth Louise Baker, Moritz Schauer, Stefan Sommer
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:775-783, 2025.

Abstract

We propose a new algorithm for learning a bridged diffusion process using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob’s $h$-transform, gives us a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, ours learns the score term $\nabla_x \log p(t, x; T, y)$, for given $t, y$ directly, completely avoiding the need for first learning a time-reversal. We compare the performance of our algorithm with existing methods and see that it outperforms using the (learned) time-reversals to learn the score term. The code can be found at \url{https://github.com/libbylbaker/forward_bridge.}

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-baker25a, title = {Score matching for bridges without learning time-reversals}, author = {Baker, Elizabeth Louise and Schauer, Moritz and Sommer, Stefan}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {775--783}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/baker25a/baker25a.pdf}, url = {https://proceedings.mlr.press/v258/baker25a.html}, abstract = {We propose a new algorithm for learning a bridged diffusion process using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob’s $h$-transform, gives us a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, ours learns the score term $\nabla_x \log p(t, x; T, y)$, for given $t, y$ directly, completely avoiding the need for first learning a time-reversal. We compare the performance of our algorithm with existing methods and see that it outperforms using the (learned) time-reversals to learn the score term. The code can be found at \url{https://github.com/libbylbaker/forward_bridge.}} }
Endnote
%0 Conference Paper %T Score matching for bridges without learning time-reversals %A Elizabeth Louise Baker %A Moritz Schauer %A Stefan Sommer %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-baker25a %I PMLR %P 775--783 %U https://proceedings.mlr.press/v258/baker25a.html %V 258 %X We propose a new algorithm for learning a bridged diffusion process using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob’s $h$-transform, gives us a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, ours learns the score term $\nabla_x \log p(t, x; T, y)$, for given $t, y$ directly, completely avoiding the need for first learning a time-reversal. We compare the performance of our algorithm with existing methods and see that it outperforms using the (learned) time-reversals to learn the score term. The code can be found at \url{https://github.com/libbylbaker/forward_bridge.}
APA
Baker, E.L., Schauer, M. & Sommer, S.. (2025). Score matching for bridges without learning time-reversals. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:775-783 Available from https://proceedings.mlr.press/v258/baker25a.html.

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