DCGC: Draft-Conditioned Global Correction for Complex Reasoning with Masked Diffusion Models

Large language models increasingly tackle tasks that require multi-step reasoning, where errors in intermediate claims can affect the final answer. Self-consistency (SC) improves reasoning by voting over sampled final answers, but its vote leaves intermediate disagreements unresolved. To address this problem, we introduce DDRG (Disagreement-Driven Verification Guided by Reasoning Graphs), a framework for selective correction from a frozen bank of reasoning traces. Our insight is that graph alignment can expose claim-level disagreements and provide correction evidence without expanding the sampled trace bank. DDRG builds source-grounded claim graphs and sends localized conflicts to an answer-blind verifier. A verifier-supported refutation that reaches the majority answer's supporting path triggers one focused repair; otherwise, DDRG returns the exact SC vote. Experimental results across five benchmarks show that native zero-shot DDRG improves macro-average accuracy over direct answering by 8.65 and 15.83 percentage points for Qwen2.5-7B and Llama3.1-8B. It also exceeds CoT, the evaluated GoT and GoV question-answering adaptations, and SC on this macro metric. DDRG links local verification to selective correction without enlarging the initial candidate bank.

Large language models produce fluent but often incorrect multi-step reasoning, and naive correction methods risk degrading already-correct answers. We introduce Denoising Iterative Self-Correction (DISC), a test-time procedure that treats verification question outputs as noisy measurements of where a solution may be corrupted. Using these signals, DISC progressively reduces errors across multiple verify-judge-correct passes, analogous to traditional iterative denoising. A binary judgment gate controls correction precision by blocking rewrites that would damage already-correct answers while the verifier and corrector together repair errors. We evaluate this trade-off using two paired diagnostics: an improvement-to-degradation ratio (precision) and a repair rate (recall). Across three benchmarks (BIG-Bench Mistake, HotpotQA, GPQA Diamond) and four models, DISC dominates Chain-of-Verification and Self-Refine on the precision-recall trade-off, reaching 81.6% accuracy with 13x more improvements per degradation than Chain-of-Verification and 5x more than Self-Refine on BIG-Bench Mistake (Sonnet~4.5). On GPQA Diamond, we identify a capability floor below which judges acknowledge contradictions in evidence but cannot translate that recognition into a correction. We further show that cross-model role allocation -- assigning verification and judgment to a model different from the generator -- mitigates self-confirmation bias.

Masked diffusion language models (MDLMs) generate text by iteratively unmasking tokens from a fully masked sequence. Their standard confidence-based unmasking strategy systematically defers high-entropy logical connective tokens, degrading reasoning performance. We introduce LogicDiff, an inference-time method that replaces confidence-based unmasking with logic-role-guided unmasking. A lightweight classification head (4.2M parameters, 0.05% of the base model) predicts the logical role of each masked position (premise, connective, derived step, conclusion, or filler) from the base model's hidden states with 98.4% accuracy, and a dependency-ordered scheduler unmasks tokens in logical order. In zero-shot settings, LogicDiff improves LLaDA-8B-Instruct accuracy from 22.0% to 60.7% on GSM8K (+38.7 percentage points) and from 23.6% to 29.2% on MATH-500 (+5.6 pp), with less than 6% speed overhead. However, with 8-shot chain-of-thought prompting, the baseline reaches approximately 70% and LogicDiff provides no additional improvement. Analysis reveals that few-shot prompting implicitly resolves the same ordering problem that LogicDiff explicitly addresses, and that fixed role-based ordering can cause premature commitment to numerical values before sufficient context is available. Our results characterize the Flexibility Trap as primarily a zero-shot phenomenon and identify context-adaptive ordering as a key direction for future work.