Critique-Guided Distillation for Robust Reasoning via Refinement

Supervised fine-tuning with expert demonstrations often produces models that imitate outputs without internalizing the reasoning processes needed for robust generalization. While critique-based approaches show promise, training models to generate critiques directly, such as Critique Fine-Tuning (CFT), can lead to output-format drift and degradation of general capabilities. We propose $\textbf{C}$ritique-$\textbf{G}$uided $\textbf{D}$istillation (CGD), a training framework that decouples critique consumption from critique generation. During fine-tuning, the student is trained to refine flawed responses conditioned on teacher critiques. CGD treats critiques as a $\textit{training-time-only}$ supervision signal, encouraging internalization of error-aware reasoning: critiques guide learning but are absent at inference. Across five model families, CGD consistently outperforms CFT and standard distillation on mathematical reasoning benchmarks, yielding 7\% average improvements and gains of up to +15.0\% on AMC23 and +12.2\% on MATH-500. On challenging competition problems such as AIME24 and AIME25, CGD achieves substantially higher Pass@1 and stronger performance at low Pass@k, indicating improved reasoning quality per sample. Importantly, CGD preserves general instruction-following capabilities where CFT degrades significantly ($-$21.3\% on IFEval). These results position CGD as a practical and compute-efficient intermediate training paradigm for reasoning-centric tasks without introducing inference-time overhead.