Multi-agent collaborative perception enables autonomous systems to overcome individual sensing limits through collective intelligence. However, real-world sensor and communication corruptions severely undermine this advantage. Crucially, existing approaches treat corruptions as static perturbations or passively conform to corrupted inputs, failing to actively recover the underlying clean semantics. To address this limitation, we introduce Diff-KD, a framework that integrates diffusion-based generative refinement into teacher-student knowledge distillation for robust collaborative perception. Diff-KD features two core components: (i) Progressive Knowledge Distillation (PKD), which treats local feature restoration as a conditional diffusion process to recover global semantics from corrupted observations; and (ii) Adaptive Gated Fusion (AGF), which dynamically weights neighbors based on ego reliability during fusion. Evaluated on OPV2V and DAIR-V2X under seven corruption types, Diff-KD achieves state-of-the-art performance in both detection accuracy and calibration robustness.