Industrial activity periodically experiences breakthrough innovations in energy efficiency, but the estimated impacts of these innovations on aggregate energy use are highly varied. We develop a general equilibrium model to investigate whether this variation is determined by the structure of the economy’s input-output network. Our results show sector-specific energy efficiency improvements affect aggregate energy use through adjustments in factor markets and commodity markets, and a process of structural transformation that alters the way energy is used and produced in the economy. We link the aggregate impact of these processes with new network centrality concepts that account for the capacity of a sector to transmit and respond to efficiency innovations. In a calibrated simulation, we find variation in these centrality concepts explains between 38 and 92 percent of variation in the aggregate impacts of energy efficiency, which suggests input-output structure is a critical determinant of the aggregate effects of energy efficiency.