Path probing is essential to maintaining an efficient overlay network topology. However, the cost of complete probing can be as high as (n²) which is prohibitive in largescale overlay networks. Recently we proposed a method that trades probing overhead for inference accuracy in sparse networks such as the Internet. The method uses physical path information to infer path quality for all of the n × (n-1) overlay paths, while actually probing only a subset of the paths. In this paper we propose and evaluate a distributed approach to implementing this method. We describe a minimum diameter, link-stress bounded overlay spanning tree, which is used to collect and disseminate path quality information. All nodes in the tree collaborate to infer the quality of all paths. Simulation results show this approach can achieve a high-level of inference accuracy while reducing probing overhead and balancing link stress on the spanning tree.