Score matching for bridges without time-reversals
<|reference_start|>Score matching for bridges without time-reversals: 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 https://github.com/libbylbaker/forward_bridge.<|reference_end|>
@article{baker2024score,
    title={Score matching for bridges without time-reversals},
    author={Elizabeth L. Baker, Moritz Schauer, Stefan Sommer},
    journal={arXiv preprint arXiv:2407.15455},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.15455},
    primaryClass={stat.ML cs.LG math.PR}
}