title: Discrete Markov Bridge
summary: 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.
paper_authors._id: 683527ba3762eb8b3ea1de34
paper_authors.name: Hengli Li
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-05-27T07:51:37.403Z
paper_authors._id: 62649e2b1ed8d81e47ad9b4e
paper_authors.avatarUrl: /avatars/f33a0b727822fd2ea99dce37fbda3d17.svg
paper_authors.fullname: Li
paper_authors.type: user
paper_authors.user: henry12348
paper_authors._id: 683527ba3762eb8b3ea1de35
paper_authors.name: Yuxuan Wang
paper_authors.status: extracted_pending
paper_authors.statusLastChangedAt: 2025-05-27T02:47:22.991Z
paper_authors._id: 60b9e6837946aff342f734ae
paper_authors.avatarUrl: /avatars/a711a6aa35757dfd7b78b26098a964fc.svg
paper_authors.fullname: Yuxuan Wang
paper_authors.type: user
paper_authors.user: ColorfulAI
paper_authors._id: 683527ba3762eb8b3ea1de36
paper_authors.name: Song-Chun Zhu
paper_authors._id: 683527ba3762eb8b3ea1de37
paper_authors.name: Ying Nian Wu
paper_authors._id: 683527ba3762eb8b3ea1de38
paper_authors.name: Zilong Zheng
paper_authors.status: extracted_pending
paper_authors.statusLastChangedAt: 2025-05-27T02:47:22.991Z
paper_authors._id: 63a95a6a7930fa8c7dd63d4e
paper_authors.avatarUrl: /avatars/d9d0420f7ddfe2f3a7e029fb05f1c89f.svg
paper_authors.fullname: Zilong Zheng
paper_authors.type: user
paper_authors.user: zlzheng
paper_title: Discrete Markov Bridge
paper_summary: 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.
paper_ai_summary: A novel framework, Discrete Markov Bridge, is introduced for discrete data modeling with Matrix Learning and Score Learning components, demonstrating superior performance compared to existing methods on Text8 and CIFAR-10 datasets.
paper_ai_keywords: discrete diffusion variational methods Discrete Markov Bridge Matrix Learning Score Learning Evidence Lower Bound ELBO