Revision Breaks Monotone Decoding: Termination and Progress in Diffusion Language Models
Srinivas Harish
Abstract
Masked diffusion language models normally decode monotonically, with masked positions becoming committed and never returning to the masked state. Self-correction methods break this invariant by allowing committed tokens to be revoked and regenerated. We study the resulting revision dynamics and show that termination is no longer automatic. Confidence-threshold revision can self-invalidate immediately when commit and revoke thresholds overlap; ordering the thresholds consistently removes this failure but still permits interleaved cycles, while confidence-gated revealing can deadlock with masks remaining. We then identify the missing progress condition. Any live revision decoder in which every rollback consumes a finite credit terminates after at most $L+B$ reveal rounds for sequence length $L$ and total revision budget $B$; a per-position budget, a strict net-progress guard, and a finite schedule are three realizations. We further show that confidence-only revision has no distribution-free quality guarantee and derive an error-enrichment condition under which a revision trigger has positive expected value. On a 40-instance mechanism screen at the selected $(.6,.8)$ threshold pair, raw confidence revision without a rollback certificate completes $17.5\%$ of runs within 64 rounds and repeats a decoder state in $82.5\%$, whereas credit, guard, and schedule controls all complete. Its raw trigger has error enrichment $E=1.003$, and $99.95\%$ of resolved revisions leave correctness unchanged. These results support requiring an explicit rollback progress certificate and measuring whether the trigger is enriched for errors.
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