Continuous-Time Discrete Markov Bridge

ICLR 2026 Conference Submission15357 Authors

Keywords: Discrete Diffusion, Diffusion Model, Markov Chain, unsupervised learning, machine learning

TL;DR: We propose a new kind of discrete diffusion model, named Discrete Markov Bridge, which perform bidirectional optimization with a new rate transition matrix.

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 \textbf{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.

Primary Area: generative models

Submission Number: 15357