Elamur Research⌕
☰
home / papers / 2026 / DecoCal: Decoding with Calibration in Diffusion Large Language Models

DecoCal: Decoding with Calibration in Diffusion Large Language Models

Paper · 2026 · Fan Xu, Huixuan Zhang and Xiaojun Wan

Summary

Diffusion large language models (DLLMs) such as LLaDA and Dream write text by repeatedly filling in masked tokens. This creates a choice that autoregressive decoding avoids: at every step the decoder must pick which positions to fix and whether to undo earlier picks. Common policies rely only on the current step's probabilities. Those probabilities often swing between steps or are inflated early, so errors get locked in. The authors propose DecoCal, an inference-time, model-agnostic decoding scheme that keeps a running, smoothed distribution for every position. Each new prediction is blended with this running estimate in log space, and the blending weight depends on how far the two diverge (KL). A token is revealed only once it passes a confidence threshold and a consistency check. Tokens that later appear premature are masked again, with a cool-down and a limit on repeated remasking, and a fallback guarantees progress. On several DLLMs and benchmarks, DecoCal improves accuracy over existing decoding strategies in most cases. This suggests that tracking confidence over time is important for diffusion-based generation.

Key points

  • Calibration rule: weight w_t = σ(γ·KL(p_t ‖ q_{t−1})), and the new estimate q_t is a softmax over a w_t-weighted mix of log q_{t−1} and log p_t (a geometric aggregation).
  • The method has three stages: calibration, unmasking gated by both confidence and consistency checks, and remasking with a cool-down. Code is released at github.com/pku0xff/DecoCal.
  • Four hyperparameters must be set: the confidence cutoff A, the KL scaling factor γ, K (the cap on how many times a token may be remasked), and the cool-down length C. These need tuning per task.
  • Total steps are capped at T·(K+1), but the method offers no exact per-sample step or latency control.
  • In a GSM8K case study with LLaDA-1.5, decoding without calibration committed the wrong answer 96 early (around step 42 of 89). DecoCal reached the correct answer, 104.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Peking UniversityBeijing · China315 works · 43,268 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 works

🧭 Topics 1Research subjects and languages the work is about.Language models & pretraining · 3,894 works

Cite

Cite as Fan Xu, Huixuan Zhang and Xiaojun Wan. 2026. DecoCal: Decoding with Calibration in Diffusion Large Language Models. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.acl-long.545

@inproceedings{xu2026decocal,
  title = {{DecoCal: Decoding with Calibration in Diffusion Large Language Models}},
  author = {Fan Xu, Huixuan Zhang and Xiaojun Wan},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.545},
  url = {https://doi.org/10.18653/v1/2026.acl-long.545}
}

References

33 references, 16 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne Van Den Berg. 2021a. Structured denoising diffusion models in discrete state-spaces. Advances in neural information processing systems, 34:17981–17993.
  2. Jacob Austin, Augustus Odena, Maxwell I. Nye, Maarten Bosma, Henryk Michalewski, David Dohan, Ellen Jiang, Carrie J. Cai, Michael Terry, Quoc V. Le, and Charles Sutton. 2021b. Program synthesis with large language models. CoRR, abs/2108.07732.
  3. Huiwen Chang, Han Zhang, Lu Jiang, Ce Liu, and William T Freeman. 2022. Maskgit: Masked generative image transformer. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11315–11325. find
  4. Kecheng Chen, Ziru Liu, Xijia Tao, Hui Liu, Xinyu Fu, Suiyun Zhang, Dandan Tu, Lingpeng Kong, Rui Liu, and Haoliang Li. 2025. Beyond confidence: Adaptive and coherent decoding for diffusion language models. arXiv preprint arXiv:2512.02044. — [arXiv:2512.02044](https://arxiv.org/abs/2512.02044) find
  5. Mark Chen. 2021. Evaluating large language models trained on code. arXiv preprint arXiv:2107.03374.
  6. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. 2021. Training verifiers to solve math word problems. CoRR, abs/2110.14168.
  7. Florinel-Alin Croitoru, Vlad Hondru, Radu Tudor Ionescu, and Mubarak Shah. 2023. Diffusion models in vision: A survey. IEEE transactions on pattern analysis and machine intelligence, 45(9):10850– 10869. find
  8. Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019. BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies,…
  9. Marjan Ghazvininejad, Omer Levy, Yinhan Liu, and Luke Zettlemoyer. 2019. Mask-predict: Parallel decoding of conditional masked language models. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Pro…
  10. Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q Weinberger. 2017. On calibration of modern neural networks. In International conference on machine learning, pages 1321–1330. PMLR. find
  11. Haoyu He, Katrin Renz, Yong Cao, and Andreas Geiger. 2025. Mdpo: Overcoming the training-inference divide of masked diffusion language models. arXiv preprint arXiv:2508.13148. — [arXiv:2508.13148](https://arxiv.org/abs/2508.13148) find
  12. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. 2021. Measuring mathematical problem solving with the math dataset. arXiv preprint arXiv:2103.03874.
  13. Zheng Huang, Kiran Ramnath, Yueyan Chen, Aosong Feng, Sangmin Woo, Balasubramaniam Srinivasan, Zhichao Xu, Kang Zhou, Shuai Wang, Haibo Ding, and Lin Lee Cheong. 2025. Diffusion language model inference with monte carlo tree search. Preprint, arXiv:2512.12168. find
  14. Mandar Joshi, Eunsol Choi, Daniel Weld, and Luke Zettlemoyer. 2017. TriviaQA: A large scale distantly supervised challenge dataset for reading comprehension. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1601–1611, Vancouver…
  15. Jungo Kasai, James Cross, Marjan Ghazvininejad, and Jiatao Gu. 2020. Non-autoregressive machine translation with disentangled context transformer. In International conference on machine learning, pages 5144–5155. PMLR. find
  16. Jaeyeon Kim, Kulin Shah, Vasilis Kontonis, Sham Kakade, and Sitan Chen. 2025. Train for the worst, plan for the best: Understanding token ordering in masked diffusions. arXiv preprint arXiv:2502.06768. — [arXiv:2502.06768](https://arxiv.org/abs/2502.06768) find
  17. Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. 2023. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation. arXiv preprint arXiv:2302.09664.
  18. Pengxiang Li, Yefan Zhou, Dilxat Muhtar, Lu Yin, Shilin Yan, Li Shen, Yi Liang, Soroush Vosoughi, and Shiwei Liu. 2025a. Diffusion language models know the answer before decoding. arXiv preprint arXiv:2508.19982. — [arXiv:2508.19982](https://arxiv.org/abs/2508.19982) find
  19. Tianyi Li, Mingda Chen, Bowei Guo, and Zhiqiang Shen. 2025b. A survey on diffusion language models. arXiv preprint arXiv:2508.10875. — [arXiv:2508.10875](https://arxiv.org/abs/2508.10875) find
  20. Xiang Li, John Thickstun, Ishaan Gulrajani, Percy S Liang, and Tatsunori B Hashimoto. 2022. Diffusion-lm improves controllable text generation. Advances in neural information processing systems, 35:4328– 4343.
  21. Justin Lovelace, Varsha Kishore, Chao Wan, Eliot Shekhtman, and Kilian Q Weinberger. 2023. Latent diffusion for language generation. Advances in Neural Information Processing Systems, 36:56998– 57025. find
  22. Shen Nie, Fengqi Zhu, Zebin You, Xiaolu Zhang, Jingyang Ou, Jun Hu, Jun Zhou, Yankai Lin, Ji-Rong Wen, and Chongxuan Li. 2025. Large language diffusion models. arXiv preprint arXiv:2502.09992.
  23. Ilya Sutskever, Oriol Vinyals, and Quoc V Le. 2014. Sequence to sequence learning with neural networks. Advances in neural information processing systems, 27.
  24. Runchu Tian, Junxia Cui, Xueqiang Xu, Feng Yao, and Jingbo Shang. 2025. Finish first, perfect later: Test-time token-level cross-validation for diffusion large language models. arXiv preprint arXiv:2510.05090. — [arXiv:2510.05090](https://arxiv.org/abs/2510.05090) find
  25. Deng-Bao Wang, Lei Feng, and Min-Ling Zhang. 2021. Rethinking calibration of deep neural networks: Do not be afraid of overconfidence. Advances in Neural Information Processing Systems, 34:11809–11820. find
  26. Guanghan Wang, Yair Schiff, Subham Sekhar Sahoo, and Volodymyr Kuleshov. 2025a. Remasking discrete diffusion models with inference-time scaling. Preprint, arXiv:2503.00307. — [arXiv:2503.00307](https://arxiv.org/abs/2503.00307) find
  27. Wen Wang, Bozhen Fang, Chenchen Jing, Yongliang Shen, Yangyi Shen, Qiuyu Wang, Hao Ouyang, Hao Chen, and Chunhua Shen. 2025b. Time is a feature: Exploiting temporal dynamics in diffusion language models. arXiv preprint arXiv:2508.09138. — [arXiv:2508.09138](https://arxiv.org/abs/2508.09138) find
  28. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2022. Self-consistency improves chain of thought reasoning in language models. arXiv preprint arXiv:2203.11171.
  29. Yijun Xiao and William Yang Wang. 2021. On hallucination and predictive uncertainty in conditional language generation. In Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume, pages 2734–2744, Online. Association for Computational…
  30. Ling Yang, Zhilong Zhang, Yang Song, Shenda Hong, Runsheng Xu, Yue Zhao, Wentao Zhang, Bin Cui, and Ming-Hsuan Yang. 2023. Diffusion models: A comprehensive survey of methods and applications. ACM computing surveys, 56(4):1–39. find
  31. Jiacheng Ye, Zhihui Xie, Lin Zheng, Jiahui Gao, Zirui Wu, Xin Jiang, Zhenguo Li, and Lingpeng Kong. 2025. Dream 7b: Diffusion large language models. arXiv preprint arXiv:2508.15487.
  32. Fengqi Zhu, Rongzhen Wang, Shen Nie, Xiaolu Zhang, Chunwei Wu, Jun Hu, Jun Zhou, Jianfei Chen, Yankai Lin, Ji-Rong Wen, and Chongxuan Li. 2025a. Llada 1.5: Variance-reduced preference optimization for large language diffusion models. Preprint, arXiv:2505.19223.
  33. Qinglin Zhu, Yizhen Yao, Runcong Zhao, Yanzheng Xiang, Amrutha Saseendran, Chen Jin, Philip Teare, Bin Liang, Yulan He, and Lin Gui. 2025b. Latent refinement decoding: Enhancing diffusion-based language models by refining belief states. arXiv preprint arXiv:2510.11052. — [arXiv:2510.11052](https://arxiv.org/abs/2510.11052) find

Updated

↑ back to top

This page in Markdown → https://md.research.elamur.ai/free/en/papers/xu-2026-decocal-decoding-calibration-diffusion-large/