Schrödinger Bridge Flow for Unpaired Data Translation

• URL: http://arxiv.org/abs/2409.09347v1
• Date: Sat, 14 Sep 2024 07:34:30 GMT
• Title: Schrödinger Bridge Flow for Unpaired Data Translation
• Authors: Valentin De Bortoli, Iryna Korshunova, Andriy Mnih, Arnaud Doucet,
• Abstract summary: We propose a novel algorithm to compute the Schr"odinger Bridge, a dynamic entropy-regularised version of Optimal Transport (OT) maps. This algorithm corresponds to a discretisation of a flow of path measures, which we call the Schr"odinger Bridge Flow. We demonstrate the performance of our algorithm on a variety of unpaired data translation tasks.
• Score: 38.19632736212184
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger Bridge Flow, whose only stationary point is the Schr\"odinger Bridge. We demonstrate the performance of our algorithm on a variety of unpaired data translation tasks.

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