Aligned Diffusion Schrödinger Bridges
This work addresses the challenge of modeling stochastic dynamics with aligned data in fields like biology, representing an incremental advancement by adapting existing theories to a specific bottleneck.
The paper tackles the problem of solving Diffusion Schrödinger Bridges (DSB) by incorporating data alignment, a structure common in biological phenomena, leading to a simpler training procedure with lower variance and sizeable improvements in tasks like predicting protein conformational changes and cellular differentiation.
Diffusion Schrödinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms for solving DSBs have so far failed to utilize the structure of aligned data, which naturally arises in many biological phenomena. In this paper, we propose a novel algorithmic framework that, for the first time, solves DSBs while respecting the data alignment. Our approach hinges on a combination of two decades-old ideas: The classical Schrödinger bridge theory and Doob's $h$-transform. Compared to prior methods, our approach leads to a simpler training procedure with lower variance, which we further augment with principled regularization schemes. This ultimately leads to sizeable improvements across experiments on synthetic and real data, including the tasks of predicting conformational changes in proteins and temporal evolution of cellular differentiation processes.