Anchor and Follower: Narrowing Valid Answers for Parallel Decoding in Diffusion Language Models

Diffusion large language models (dLLMs) can accelerate decoding by committing tokens at multiple masked positions in parallel. However, when multiple valid answers remain compatible with the current context, parallel commitment can mix tokens from different answers and produce an output consistent with none of them. Sequential decoding reduces this risk by refining between commitments, suggesting a view of denoising as progressively narrowing the set of compatible valid answers. To study how predictions over valid answers change during denoising, we introduce *valid answer uncertainty* $N_t$. Across a controlled graph task and three ParallelBench tasks, we find that commitments differ sharply in their effect on $N_t$. Commitments that distinguish among the remaining valid answers can substantially reduce it, while shared commitments change it little. Intermediate refinement tends to reduce it further. Building on these findings, we propose **Anchor and Follower (AnF)**, a training-free decoding method that selects an anchor whose commitment can guide subsequent refinement toward lower answer uncertainty. AnF then commits the anchor, refines the remaining predictions, and commits high-confidence followers in parallel, combining sequential refinement with parallel efficiency. With LLaDA-8B-Instruct, AnF achieves 16.9% higher accuracy with 31.0% fewer NFEs than DAPD on HumanEval and the highest accuracy among compared methods on HumanEval, MBPP, and IFEval.