MOTIVATION: It has long been hypothesized that incorporating models of network noise as well as edge directions and known pathway information into the representation of protein-protein interaction (PPI) networks might improve their utility for functional inference. However, a simple way to do this has not been obvious. We find that diffusion state distance (DSD), our recent diffusion-based metric for measuring dissimilarity in PPI networks, has natural extensions that incorporate confidence, directions and can even express coherent pathways by calculating DSD on an augmented graph. RESULTS: We define three incremental versions of DSD which we term cDSD, caDSD and capDSD, where the capDSD matrix incorporates confidence, known directed edges, and pathways into the measure of how similar each pair of nodes is according to the structure of the PPI network. We test four popular function prediction methods (majority vote, weighted majority vote, multi-way cut and functional flow) using these different matrices on the Baker's yeast PPI network in cross-validation. The best performing method is weighted majority vote using capDSD. We then test the performance of our augmented DSD methods on an integrated heterogeneous set of protein association edges from the STRING database. The superior performance of capDSD in this context confirms that treating the pathways as probabilistic units is more powerful than simply incorporating pathway edges independently into the network. AVAILABILITY: All source code for calculating the confidences, for extracting pathway information from KEGG XML files, and for calculating the cDSD, caDSD and capDSD matrices are available from http://dsd.cs.tufts.edu/capdsd