Screens for epistatic interactions have long been used to characterize functional relationships corresponding to protein complexes, metabolic pathways, and other functional modules. Although epistasis between adaptive mutations is also common in laboratory evolution experiments, the functional basis for these interactions is less well characterized. Here, we quantify the extent to which gene function (as determined by a genome-wide screen for epistasis among deletion mutants) influences the rate and genetic basis of compensatory adaptation in a set of 37 gene deletion mutants nested within 16 functional modules. We find that functional module has predictive power: mutants with deletions in the same module tend to adapt more similarly, on average, than those with deletions in different modules. At the same time, initial fitness also plays a role: independent of the specific functional modules involved, adaptive mutations tend to be systematically more beneficial in less-fit genetic backgrounds, consistent with a general pattern of diminishing returns epistasis. We measured epistatic interactions between initial gene deletion mutations and the mutations that accumulate during compensatory adaptation and found a general trend towards positive epistasis (i.e. mutations tend to be more beneficial in the background in which they arose). In two functional modules, epistatic interactions between the initial gene deletions and the mutations in their descendant lines caused evolutionary entrenchment, indicating an intimate functional relationship. Our results suggest that genotypes with similar epistatic interactions with gene deletion mutations will also have similar epistatic interactions with adaptive mutations, meaning that genome scale maps of epistasis between gene deletion mutations can be predictive of evolutionary dynamics.