Score Matching for Bridges Without Learning Time-Reversals
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
Text
Baker et al. "Score Matching for Bridges Without Learning Time-Reversals." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.Markdown
[Baker et al. "Score Matching for Bridges Without Learning Time-Reversals." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.](https://mlanthology.org/aistats/2025/baker2025aistats-score/)BibTeX
@inproceedings{baker2025aistats-score,
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},
year = {2025},
pages = {775-783},
volume = {258},
url = {https://mlanthology.org/aistats/2025/baker2025aistats-score/}
}