Diffusion language models (DLMs) expose a provisional prediction at every denoising step, creating an opportunity for generation-time early exit that stops decoding before the schedule is exhausted. Existing early-exit gates decide termination from fixed-region confidence statistics or schedule-dependent rules, evidence too coarse for a decision that freezes every remaining position at once, so they fire prematurely on long chain-of-thought outputs whose answers stabilize only near the end. Adaptive sampling, the other axis of training-free acceleration, paces how quickly positions commit while decoding continues but never verifies that the output itself has stabilized. We introduce a training-free, candidate-aware early-exit framework that keeps the two axes separate and matches each decision to evidence of its own scope. Confidence-Verified Commit (CVC) governs when the sequence may stop by verifying confidence and sustained argmax stability over the dynamically extracted candidate span using a deterministic parser specified from each task's output format. Block-Wise Early Commit (BWEC) governs where to accelerate by applying a cheaper local rule to non-final blocks, while leaving the final block and global termination under CVC. We refer to their combination as LATCH (Localized Acceleration with Tracked-Candidate Halting). Unlike prior methods, LATCH needs no suffix-prompt construction; it is prompt-anchor-free but format-aware. We evaluate LATCH end to end on 11 tasks under zero-shot settings using LLaDA and Dream. LATCH stays within 2.0 percentage points of full-decoding accuracy across all 22 evaluation settings, with one frozen hyperparameter set that transfers cross-backbone untuned, while achieving end-to-end TPS speedups of 9.3-17.8x on short-answer tasks and 2.0-3.3x on long-reasoning tasks.

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