With minimal compromises on other metrics, eliminating overflow and lowering congestion level of global routing results as much as possible is a crucial topic for reducing violations and hotspots in subsequent design phases. Different from current common practices of using maze routing according to some explicit orders to sequentially re-route particular nets of interest, this paper proposes a collaborative refinement framework that can generate multiple paths simultaneously to enlarge the solution space based on a multi-agent generative model, serving as a flexible post-processing plug-in on existing global routing results to reduce congestion. Experimental results well reveal its effectiveness.