Score matching for bridges without time-reversals

Paper in proceeding, 2025

We propose a new algorithm for learning bridged diffusion processes using scorematching 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, yields a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, we learn the score term ∇xlogp(t,x;T,y) directly, for given t,y, completely avoiding first learning a timereversal. 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.