Entering the Era of Discrete Diffusion Models: A Benchmark for Schrödinger Bridges and Entropic Optimal Transport
Existing discrete diffusion and flow models lack reliable evaluation methods for solving entropy-regularized optimal transport (EOT) and Schrödinger bridge (SB) problems. Method: We introduce the first discrete SB benchmark framework with closed-form analytical solutions, enabling precise and reproducible validation of discrete diffusion models. We propose two efficient algorithms—DLightSB and DLightSB-M—and extend them to α-CSBM, enabling the first systematic evaluation of discrete-domain SB methods. Leveraging EOT theory and dynamic SB solvers, we construct multiple high-dimensional analytically tractable probability distribution pairs and conduct comprehensive performance comparisons of both classical and novel solvers under unified experimental settings. Contribution/Results: This work fills a critical gap in interpretable evaluation for discrete generative models and establishes essential infrastructure for grounding SB theory in practice. Our benchmark and algorithms facilitate rigorous, transparent, and reproducible assessment of discrete SB-based generative modeling, advancing both theoretical understanding and empirical development.