Score matching for bridges without learning time-reversals

Elizabeth Louise Baker, Moritz Schauer, Stefan Sommer

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 https://github.com/libbylbaker/forward_bridge.

Submission Number: 273