[2509.23348] Entering the Era of Discrete Diffusion Models: A Benchmark for Schrödinger Bridges and Entropic Optimal Transport

Computer Science > Machine Learning arXiv:2509.23348 (cs) [Submitted on 27 Sep 2025 (v1), last revised 2 Mar 2026 (this version, v2)] 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 View a PDF of the paper titled Entering the Era of Discrete Diffusion Models: A Benchmark for Schr\"odinger Bridges and Entropic Optimal Transport, by Xavier Aramayo Carrasco and 4 other authors View PDF HTML (experimental) Abstract:The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schrödinger 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 remains no reliable way to assess 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 benchma...