Multi-channel speech enhancement aims to recover clean speech from noisy multi-channel recordings. Most deep learning methods employ discriminative training, which can lead to non-linear distortions from regression-based objectives, especially under challenging environmental noise conditions. Inspired by ArrayDPS for unsupervised multi-channel source separation, we introduce ArrayDPS-Refine, a method designed to enhance the outputs of discriminative models using a clean speech diffusion prior. ArrayDPS-Refine is training-free, generative, and array-agnostic. It first estimates the noise spatial covariance matrix (SCM) from the enhanced speech produced by a discriminative model, then uses this estimated noise SCM for diffusion posterior sampling. This approach allows direct refinement of any discriminative model's output without retraining. Our results show that ArrayDPS-Refine consistently improves the performance of various discriminative models, including state-of-the-art waveform and STFT domain models. Audio demos are provided at https://xzwy.github.io/ArrayDPSRefineDemo/.