# Decoding in Order-Agnostic Language Models: Chain-Rule Deviation and Uniform Spreading

arXiv: https://arxiv.org/abs/2606.00997 · HTML: https://mlsanity.com/paper/2606.00997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 31 May 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 27 of 27)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [CMATH: Can Your Language Model Pass Chinese Elementary School Math Test?](https://mlsanity.com/paper/2306.16636/) (2023)
- [LLaDA2.1: Speeding Up Text Diffusion via Token Editing](https://mlsanity.com/paper/2602.08676/) (2026)
- [Deferred Commitment Decoding for Diffusion Language Models](https://mlsanity.com/paper/2601.02076/) (2026)
- [Parallelism and Generation Order in Masked Diffusion Language Models: Limits Today, Potential Tomorrow](https://mlsanity.com/paper/2601.15593/) (2026)
- [Improving Diffusion Language Model Decoding through Joint Search in Generation Order and Token Space](https://mlsanity.com/paper/2601.20339/) (2026)
- [Generation Order and Parallel Decoding in Masked Diffusion Models: An Information-Theoretic Perspective](https://mlsanity.com/paper/2602.00286/) (2026)
- [Where-to-Unmask: Ground-Truth-Guided Unmasking Order Learning for Masked Diffusion Language Models](https://mlsanity.com/paper/2602.09501/) (2026)
- [Improving Sampling for Masked Diffusion Models via Information Gain](https://mlsanity.com/paper/2602.18176/) (2026)
- [Optimizing Decoding Paths in Masked Diffusion Models by Quantifying Uncertainty](https://mlsanity.com/paper/2512.21336/) (2025)
- [Auto-Regressive Masked Diffusion Models](https://mlsanity.com/paper/2601.16971/) (2026)

## Abstract (arXiv)

Order-agnostic language models (OALMs), including discrete diffusion language models (dLLMs), are trained to predict masked tokens under arbitrary conditioning sets, allowing sequences to be generated or scored under arbitrary reveal orders at inference time. In LLaDA-2.1, we report three findings. First, the learned conditionals are not exact factorizations of a coherent joint distribution: changing only the reveal order shifts target log-likelihood by up to 0.49 nats/token, so likelihood alone mixes content difficulty with path-dependent artifacts. Second, although confidence-first (CF) decoding is order-agnostic, its reveal orders are close to left-to-right (L2R) on content tokens. Third, we propose a complementary diagnostic based on the shape of the confidence trace. A uniform-spreading theorem shows that, at fixed total likelihood, target recoverability is maximized when per-step confidence is spread uniformly; the resulting deviation motivates Var(log qt) as a diagnostic for comparing decoding paths. Across C4 and four downstream benchmarks, low variance separates structured paths from random ordering, and variance is consistently associated with downstream correctness. These results support reporting mean confidence and confidence variance jointly when comparing OALM decoding paths.