Half of the sun's power lies in the infrared. As a result, the optimal bandgaps for solar cells in both the single-junction and even the tandem architectures lie beyond 850 nm. However, progress in low-cost, large-area, physically flexible solar cells has instead been made in organic and polymer materials possessing absorption onsets in the visible. Recent advances have been achieved in solution-cast infrared photovoltaics through the use of colloidal quantum dots. Here we report stable solution-processed photovoltaic devices having 3.6% power conversion efficiency in the infrared. The use of a strongly bound bidentate linker, benzenedithiol, ensures device stability over weeks. The devices reach external quantum efficiencies of 46% in the infrared and 70% across the visible. We investigate in detail the physical mechanisms underlying the operation of this class of device. In contrast with drift-dominated behavior in recent reports of PbS quantum dot photovoltaics, we find that diffusion of electrons and holes over hundreds of nanometers through our PbSe colloidal quantum dot solid is chiefly responsible for the high external quantum efficiencies obtained in this new class of devices.