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arXiv · 2405.14449

Adversarial Schr\"odinger Bridge Matching

Nikita Gushchin·Daniil Selikhanovych·Sergei Kholkin·Evgeny Burnaev·Alexander Korotin
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Abstract

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds. We provide the code at https://github.com/Daniil-Selikhanovych/ASBM.

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Nikita Gushchin, Daniil Selikhanovych, Sergei Kholkin, Evgeny Burnaev, Alexander Korotin. 2024-05-23. Adversarial Schr\"odinger Bridge Matching. https://arxiv.org/abs/2405.14449

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