mlsanityData to 14 Oct 2026

Discrete Markov Bridge

arXiv 2505.19752 ↗First posted 26 May 2025cs.LG cs.AI cs.CLcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 34 of its 42 references that are in the map. First posted on arXiv 26 May 2025.

Builds on

34 of 42 references.

Closest ancestors · 6

Same direction, newest first

  1. 2022Score-based Continuous-time Discrete Diffusion Models30 Nov
  2. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  3. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  4. 2021Variational Diffusion Models1 Jul
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 28

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  3. 2019RoBERTa: A Robustly Optimized BERT Pretraining Approachcited by 13,372
  4. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 13,028
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  6. 2022Generative Adversarial Networkscited by 5,627
  7. 2017Neural Discrete Representation Learningcited by 4,712
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  9. 2019ALBERT: A Lite BERT for Self-supervised Learning of Language Representationscited by 2,790
  10. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,626
  11. 2015Variational Inference with Normalizing Flowscited by 2,170
  12. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
16 more
  1. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  2. 2020Training Generative Adversarial Networks with Limited Datacited by 1,186
  3. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,027
  4. 2025Large Language Diffusion Modelscited by 912
  5. 2016Conditional Image Generation with PixelCNN Decoderscited by 862
  6. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 745
  7. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  8. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 405
  9. 2024Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Samplingcited by 208
  10. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 148
  11. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  12. 2020Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Samplingcited by 71
  13. 2019Discrete Flows: Invertible Generative Models of Discrete Datacited by 68
  14. 2019Latent Normalizing Flows for Discrete Sequencescited by 67
  15. 2022Training and Inference on Any-Order Autoregressive Models the Right Waycited by 64
  16. 2018Autoregressive Quantile Networks for Generative Modelingcited by 31

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  4. 2026Sample complexity bounds for categorical Markov random fields via Discrete Diffusions
  5. 2026Bridge Graphical Models: Coupling, Projection, and Current-Preserving Dynamics for Generative Modeling
  6. 2024Unified Discrete Diffusion for Categorical Data
  7. 2024Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis
  8. 2024Discrete Modeling via Boundary Conditional Diffusion Processes