The molecular and clinical features of a complex disease can be influenced by other diseases affecting the same individual. Understanding disease-disease interactions is therefore crucial for revealing shared molecular mechanisms among diseases and designing effective treatments. Here we introduce Flow Centrality (FC), a network-based approach to identify the genes mediating the interaction between two diseases in a protein-protein interaction network. We focus on asthma and COPD, two chronic respiratory diseases that have been long hypothesized to share common genetic determinants and mechanisms. We show that FC highlights potential mediator genes between the two diseases, and observe similar outcomes when applying FC to 66 additional pairs of related diseases. Further, we perform in vitro perturbation experiments on a widely replicated asthma gene, GSDMB, showing that FC identifies candidate mediators of the interactions between GSDMB and COPD-associated genes. Our results indicate that FC predicts promising gene candidates for further study of disease-disease interactions.