2024/09/14 by Valentin De Bortoli, Iryna Korshunova, De Bortoli, Valentin +5 · 2 voices · 19 citations
Chemistry · Computer Science · Engineering · Mathematics · Medicine · Physics and Astronomy · #Anatomy #Bridge (graph theory) #Chemistry #Computer science #Flow (mathematics) #Lattice Boltzmann Simulation Studies #Mechanics #Medicine #Model Reduction and Neural Networks #Music and Audio Processing #Physics #Translation (biology) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2409.09347
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Mass transport problems arise in many areas of machine learning whereby one wants to compute a map transporting one distribution to another. Generative modeling techniques like Generative Adversarial Networks (GANs) and Denoising Diffusion Models (DDMs) have been successfully adapted to solve such transport problems, resulting in CycleGAN and Bridge Matching respectively. However, these methods do not approximate Optimal Transport (OT) maps, which are known to have desirable properties. Existing techniques approximating OT maps for high-dimensional data-rich problems, such as DDM-based Rectified Flow and Schrödinger Bridge procedures, require fully training a DDM-type model at each iteration, or use mini-batch techniques which can introduce significant errors. We propose a novel algorithm to compute the Schrödinger Bridge, a dynamic entropy-regularised version of OT, that eliminates the need to train multiple DDM-like models. This algorithm corresponds to a discretisation of a flow of path measures, which we call the Schrödinger Bridge Flow, whose only stationary point is the Schrödinger Bridge. We demonstrate the performance of our algorithm on a variety of unpaired data translation tasks.