Entering the Era of Discrete Diffusion Models: A Benchmark for Schrödinger Bridges and Entropic Optimal Transport

• URL: http://arxiv.org/abs/2509.23348v1
• Date: Sat, 27 Sep 2025 14:51:07 GMT
• Title: Entering the Era of Discrete Diffusion Models: A Benchmark for Schrödinger Bridges and Entropic Optimal Transport
• Authors: Xavier Aramayo Carrasco, Grigoriy Ksenofontov, Aleksei Leonov, Iaroslav Sergeevich Koshelev, Alexander Korotin,
• Abstract summary: We introduce a benchmark for the Schr"odinger bridge (SB) problem on discrete spaces.<n>Our construction yields pairs of probability distributions with analytically known SB solutions, enabling rigorous evaluation.<n>This work provides the first step toward proper evaluation of SB methods on discrete spaces.
• Score: 46.28885837515665
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent advances in discrete diffusion and flow models have sparked growing interest in applying SB methods to discrete domains, there is still no reliable way to evaluate how well these methods actually solve the underlying problem. We address this challenge by introducing a benchmark for SB on discrete spaces. Our construction yields pairs of probability distributions with analytically known SB solutions, enabling rigorous evaluation. As a byproduct of building this benchmark, we obtain two new SB algorithms, DLightSB and DLightSB-M, and additionally extend prior related work to construct the $\alpha$-CSBM algorithm. We demonstrate the utility of our benchmark by evaluating both existing and new solvers in high-dimensional discrete settings. This work provides the first step toward proper evaluation of SB methods on discrete spaces, paving the way for more reproducible future studies.

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