Cord: Confidence-Anchored Order Residual Decoding for Masked Diffusion Language Models

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The decoding order of masked diffusion language models (dLLMs) can substantially affect generation quality, yet common decoders typically apply the same reveal rule throughout generation. Confidence provides a strong default, but it measures how decisively a position can be predicted now, not how useful revealing that position will be for subsequent decoding. We propose Cord, a lightweight prompt-conditioned policy that retains confidence decoding as a stable reference and learns when and how to depart from it through geometric residuals over generation direction, proximity to revealed context, and two-sided infilling. The residuals adapt to both the prompt and the evolving partial response. Rather than sampling a new policy action at every decoding step, Cord samples a single low-dimensional coefficient matrix per rollout, which induces an entire state-dependent reveal trajectory. This yields a contextual-bandit formulation trained directly from sequence-level rewards, without step-level credit assignment or backbone updates. Across three dLLMs and five reasoning, code, and constraint-satisfaction benchmarks, Cord improves average task success from 32.0% under confidence decoding to 48.2%, and further improves over the best per-domain fixed residual. Behavioral audits show that the learned residuals induce substantial, task-dependent changes in reveal locality and two-sided infilling. Cord adds only $0.53$M trainable parameters, requires no additional backbone forward passes, and incurs only 5.39% inference latency overhead.