SOLVING SCHRODINGER BRIDGE PROBLEM VIA STOCHASTIC ACTION MINIMIZATION

Mykola Bordyuh, Daniel Wong, Robert Moccia, Djork-Arné Clevert

Primary Area: generative models

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Keywords: Schrodinger bridge, optimal transport, single-cell, trajectories

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TL;DR: We propose a training method for the Schrodinger bridge problem

Abstract:

The Schrodinger bridge problem is a classical entropy-regularized optimal transport problem that seeks to find optimal diffusion trajectories that transform one probability distribution into another. Although mathematical theory has reached
a mature stage, the ongoing research in algorithmic advancements remains a dynamic field, driven by recent innovations in diffusion models. We introduce stochastic Lagrangian and stochastic action as viable alter-
native for serving as a direct loss function. We demonstrate the feasibility of incorporating all the vital physical constraints necessary to solve the problem directly into the Lagrangian, providing an intuitive grasp of the loss function and streamlining the training process.

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Submission Number: 8551