TSBM: New diffusion method improves trajectory inference with twisted Brownian motion

The classical Schrödinger bridge problem seeks optimal transport dynamics between two distributions while minimizing KL divergence to a reference Markov process. Prior work, like Diffusion Schrödinger Bridge Matching (DSBM), solved this for Brownian motion with zero potential. Now, Maxence Noble and colleagues generalize this to twisted Brownian motion, where the reference process is a Feynman-Kac transform induced by a time-dependent differentiable potential. Their method, Twisted Schrödinger Bridge Matching (TSBM), builds on the Iterative Markovian Fitting (IMF) framework and extends it rigorously to handle both continuous- and discrete-time potentials.

TSBM introduces a novel bridge-matching loss that explicitly uses the gradient of the potential, recovering DSBM as a special case when the potential is zero. To stabilize training, the authors propose trajectory-based variance-reduction techniques applicable beyond this setting. Empirically, TSBM demonstrates clear benefits on high-dimensional trajectory inference tasks, including crowd navigation and single-cell data analysis. The method scales to increasingly complex settings, offering improved performance over DSBM and other baselines. Code is available on GitHub.