Discrete Markov Bridge

TL;DR

This paper introduces Discrete Markov Bridge, a new framework for discrete representation learning that enhances expressiveness and performance through matrix and score learning, with theoretical guarantees and strong empirical results.

Contribution

The paper presents Discrete Markov Bridge, a novel approach with theoretical analysis and empirical validation, improving discrete data modeling beyond fixed transition matrix methods.

Findings

Achieves an ELBO of 1.38 on Text8, outperforming baselines.

Demonstrates competitive results on CIFAR-10.

Provides theoretical guarantees and convergence analysis.

Abstract

Discrete diffusion has recently emerged as a promising paradigm in discrete data modeling. However, existing methods typically rely on a fixed rate transition matrix during training, which not only limits the expressiveness of latent representations, a fundamental strength of variational methods, but also constrains the overall design space. To address these limitations, we propose Discrete Markov Bridge, a novel framework specifically designed for discrete representation learning. Our approach is built upon two key components: Matrix Learning and Score Learning. We conduct a rigorous theoretical analysis, establishing formal performance guarantees for Matrix Learning and proving the convergence of the overall framework. Furthermore, we analyze the space complexity of our method, addressing practical constraints identified in prior studies. Extensive empirical evaluations validate the effectiveness of the proposed Discrete Markov Bridge, which achieves an Evidence Lower Bound (ELBO) of 1.38 on the Text8 dataset, outperforming established baselines. Moreover, the proposed model demonstrates competitive performance on the CIFAR-10 dataset, achieving results comparable to those obtained by image-specific generation approaches.