The yeast synthetic lethal genetic interaction network contains rich information about underlying pathways and protein complexes as well as new genetic interactions yet to be discovered. We have developed a graph diffusion kernel as a unified framework for inferring complex/pathway membership analogous to "friends" and genetic interactions analogous to "enemies" from the genetic interaction network. When applied to the Saccharomyces cerevisiae synthetic lethal genetic interaction network, we can achieve a precision around 50% with 20% to 50% recall in the genome-wide prediction of new genetic interactions, supported by experimental validation. The kernels show significant improvement over previous best methods for predicting genetic interactions and protein co-complex membership from genetic interaction data.