Reproduce “Score matching for bridges without learning time-reversals” on OpenResearch

About this paper

Elizabeth L. Baker, Moritz Schauer, Stefan Sommer

Researchers developed a score-matching algorithm that directly learns the forward-in-time score function for bridged diffusion processes, reducing computational training time by half compared to prior two-stage methods. This approach enables efficient and stable simulation of conditioned trajectories for linear and non-linear stochastic differential equations, including high-dimensional shape models.

Key insights

• Adjoint processes, which are distinct from time-reversals, offer direct access to the relevant transition densities, enabling a single-stage, more efficient learning process for forward bridges.
• By formulating a loss function based on the KL divergence between the true and learned conditioned processes and re-expressing it via adjoints, the score of the forward bridge can be learned directly and efficiently.
• Directly learning the forward bridge score function (rather than inferring it from a learned time-reversal) significantly improves computational efficiency and stability, especially in higher dimensions.

Summary by alphaXiv.