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

2025-09-27

AI Summary

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.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

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 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 $α$-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.

Problem

• Evaluating Schrödinger Bridge methods on discrete spaces
• Providing benchmark distributions with known analytical solutions
• Developing new algorithms for discrete optimal transport problems

Innovation

• Benchmark for discrete Schrödinger bridge evaluation
• New SB algorithms DLightSB and DLightSB-M
• Analytical SB solutions for rigorous method validation