Correcting flawed reasoning traces remains a significant challenge for Large Language Models (LLMs), whose autoregressive generation can propagate early mistakes into subsequent reasoning. We introduce DCGC, a Masked Diffusion Model (MDM) framework for global correction that uses an imperfect solution draft from an upstream solver as auxiliary context. DCGC combines task-specific Supervised Fine-Tuning (SFT) with a novel inference-time mechanism called Dynamic Dual-CFG. This mechanism separates problem-only and joint problem-draft branches and scales the draft-conditioned residual using a relative confidence gap. Across math, code, and knowledge reasoning benchmarks, DCGC outperforms standard sampling and simpler CFG variants, with additional results suggesting transfer to different diffusion backbones. In test-time setting where ground-truth failure labels are unavailable, DCGC improves full test set accuracy by correcting low-consensus upstream outputs, highlighting its utility as a verifier-free global correction module for difficult reasoning instances.
While recent advances in data synthesis aim to curate high-quality datasets, most generation pipelines still rely on heuristic prompt-based control. This black-box paradigm provides limited insight into how individual samples interact with a model's underlying learning dynamics. To bridge this gap, we propose a circuit-grounded framework that connects training-dynamics-based data valuation with mechanistic interpretability (MI). Specifically, we conceptualize data quality along three complementary utility axes, learnability, challenge, and alignment. First, we uncover specialized model-internal circuits that causally govern these utility signals. Then, moving beyond heuristic prompting toward mechanistic control, we leverage these circuits as controllable interfaces, actively steering generation to produce utility-targeted data. Building on this capability, we introduce SAMS (Stage-Aware Mechanistic Scheduling), which schedules circuit-steered data according to the model's evolving optimization needs. Experiments on multiple-choice QA tasks demonstrate that our approach yields precisely controlled data with greater diversity than prompt-based baselines, consistently improving downstream performance and calibration. Ultimately, this work establishes a principled white-box paradigm for interpretable data generation, pioneering the use of MI not just as an analytical tool, but as a practical, controllable interface.
