Adversarial Schr\"odinger Bridge Matching
<|reference_start|>Adversarial Schr\"odinger Bridge Matching: 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.<|reference_end|>
@article{gushchin2024adversarial,
    title={Adversarial Schr\"odinger Bridge Matching},
    author={Nikita Gushchin, Daniil Selikhanovych, Sergei Kholkin, Evgeny Burnaev,
  Alexander Korotin},
    journal={arXiv preprint arXiv:2405.14449},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14449},
    primaryClass={cs.LG}
}