# Low-Confidence Remasking Traps Flexibility: Realizing Arbitrary-Order Potential for Diverse Rollouts in Diffusion LLMs

arXiv: https://arxiv.org/abs/2609.34509 · HTML: https://mlsanity.com/paper/2609.34509/

## 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 41 of its 44 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

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

## Builds on (most cited first, 30 of 41)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [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)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Models](https://mlsanity.com/paper/2505.19223/) (2025)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [DiffuCoder: Understanding and Improving Masked Diffusion Models for Code Generation](https://mlsanity.com/paper/2506.20639/) (2025)
- [d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2504.12216/) (2025)
- [A Reparameterized Discrete Diffusion Model for Text Generation](https://mlsanity.com/paper/2302.05737/) (2023)
- [Accelerated Sampling from Masked Diffusion Models via Entropy Bounded Unmasking](https://mlsanity.com/paper/2505.24857/) (2025)
- [Dimple: Discrete Diffusion Multimodal Large Language Model with Parallel Decoding](https://mlsanity.com/paper/2505.16990/) (2025)
- [ACECODER: Acing Coder RL via Automated Test-Case Synthesis](https://mlsanity.com/paper/2502.01718/) (2025)
- [On Decoding Strategies for Neural Text Generators](https://mlsanity.com/paper/2203.15721/) (2022)
- [Revolutionizing Reinforcement Learning Framework for Diffusion Large Language Models](https://mlsanity.com/paper/2509.06949/) (2025)
- [wd1: Weighted Policy Optimization for Reasoning in Diffusion Language Models](https://mlsanity.com/paper/2507.08838/) (2025)

## Abstract (arXiv)

Masked diffusion language models support arbitrary-order generation, suggesting a natural way to produce diverse outputs. However, recent work argues that this flexibility reduces diversity by delaying high-uncertainty tokens that can lead to different generation paths. We trace this diversity loss not to arbitrary-order generation itself, but largely to low-confidence remasking (LCR), a widely used decoding rule. At each step, LCR samples a token at every masked position but commits only the sampled token with the highest probability, filtering out the rest. We show that this mechanism can exponentially suppress lower-probability tokens as more positions compete, and observe the same suppression in LLaDA. In contrast, top-probability position selection (TPP), which has often been conflated with LCR under the shared label confidence-based decoding, avoids this diversity loss. TPP first selects the position whose most likely token has the highest probability, then samples directly from that position's distribution. Replacing LCR with TPP restores diversity and yields Pass@k comparable to left-to-right decoding, suggesting that the reported diversity loss stems largely from LCR's filtering rather than from generating high-confidence positions first. To further exploit order flexibility, we introduce Entropy-Guided Initialization (EGI), which samples the first token at the highest-entropy position and then follows TPP. This simple modification further improves rollout diversity and solution coverage beyond left-to-right decoding, with gains extending to downstream policy optimization, highlighting the potential of arbitrary-order generation for diverse rollouts.