mlsanityData to 7 Oct 2026

Breaking the Factorization Barrier in Diffusion Language Models

arXiv 2603.00045 ↗First posted 9 Feb 2026cs.LG cs.AIcited by 11

On the map: Diffusion models → Discrete and text diffusion

Abstract (arXiv)

Diffusion language models theoretically allow for efficient parallel generation but are practically hindered by the ``factorization barrier'': the assumption that simultaneously predicted tokens are independent. This limitation forces a trade-off: models must either sacrifice speed by resolving dependencies sequentially or suffer from incoherence due to factorization. We argue that this barrier arises not from limited backbone expressivity, but from a structural misspecification: models are restricted to fully factorized outputs because explicitly parameterizing a joint distribution would require the Transformer to output a prohibitively large number of parameters. We propose Coupled Discrete Diffusion (CoDD), a hybrid framework that breaks this barrier by replacing the fully-factorized output distribution with a lightweight, tractable probabilistic inference layer. This formulation yields a distribution family that is significantly more expressive than standard factorized priors, enabling the modeling of complex joint dependencies, yet remains compact enough to avoid the prohibitive parameter explosion associated with full joint modeling. Empirically, CoDD seamlessly enhances diverse diffusion language model architectures with negligible overhead, matching the reasoning performance of computationally intensive Reinforcement Learning baselines at a fraction of the training cost. Furthermore, it prevents performance collapse in few-step generation, enabling high-quality outputs at significantly reduced latencies. Code available at: https://github.com/liuanji/CoDD.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Placed in Discrete and text diffusion, one of 14 directions in Diffusion models. Builds on 29 of its 37 references that are in the map. First posted on arXiv 9 Feb 2026.

Builds on

29 of 37 references.

Closest ancestors · 10

Same direction, newest first

  1. 2025Dream 7B: Diffusion Large Language Models21 Aug
  2. 2025wd1: Weighted Policy Optimization for Reasoning in Diffusion Language Models7 Jul
  3. 2025Large Language Diffusion Models14 Feb
  4. 2025Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions10 Feb
  5. 2024Energy-Based Diffusion Language Models for Text Generation28 Oct
  6. 2024Discrete Copula Diffusion2 Oct
  7. 2024Simple and Effective Masked Diffusion Language Models11 Jun
  8. 2024Simplified and Generalized Masked Diffusion for Discrete Data6 Jun
  9. 2024Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data6 Jun
  10. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution25 Oct

Other references · 19

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  3. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  4. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  5. 2022MaskGIT: Masked Generative Image Transformercited by 1,082
  6. 2025d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learningcited by 178
  7. 2025Accelerating Diffusion LLMs via Adaptive Parallel Decodingcited by 108
  8. 2023Tractable Control for Autoregressive Language Generationcited by 65
  9. 2024Distillation of Discrete Diffusion through Dimensional Correlationscited by 46
  10. 2016On the Latent Variable Interpretation in Sum-Product Networkscited by 40
  11. 2022Scaling Up Probabilistic Circuits by Latent Variable Distillationcited by 35
  12. 2024Adaptable Logical Control for Large Language Modelscited by 30
7 more
  1. 2019Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architecturescited by 24
  2. 2020Scaling Hidden Markov Language Modelscited by 22
  3. 2023Image Inpainting via Tractable Steering of Diffusion Modelscited by 22
  4. 2017Boosted Generative Modelscited by 18
  5. 2024Probabilistic Neural Circuitscited by 7
  6. 2024Faster Language Models with Better Multi-Token Prediction Using Tensor Decompositioncited by 7
  7. 2025Rethinking Probabilistic Circuit Parameter Learningcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 11.

11 papers.

Similar, not cited

Close in wording, no citation either way

  1. 2026CoDAR: Continuous Diffusion Language Models are More Powerful Than You Think
  2. 2025Coevolutionary Continuous Discrete Diffusion: Make Your Diffusion Language Model a Latent Reasoner
  3. 2025Latent-Augmented Discrete Diffusion Models
  4. 2025CtrlDiff: Boosting Large Diffusion Language Models with Dynamic Block Prediction and Controllable Generation
  5. 2026Reasoning with Latent Tokens in Diffusion Language Models
  6. 2025Perfect diffusion is mathsfTC0 -- Bad diffusion is Turing-complete
  7. 2026Beyond Mode-Seeking RL: Trajectory-Balance Post-Training for Diffusion Language Models
  8. 2026Representation-Space MMD for Diffusion Language Models