Demand for low-precision inference, including NVFP4-based approaches, has grown as large language models are increasingly deployed in latency and cost constrained production environments. Quantization-aware distillation (QAD) helps recover accuracy lost under low bit quantization by training a quantized student to match the output distribution of a frozen higher precision teacher via a KL-divergence loss. In this work, we first provide a representation level diagnosis of QAD: output matching alo...