Image relighting is the task of showing what a scene from a source image would look like if illuminated differently. Inverse graphic schemes recover an explicit representation of geometry and a set of chosen intrinsics, then relight with some form of renderer. But error control for inverse graphics is difficult, and inverse graphics methods can represent only the effects of the chosen intrinsics. This paper describes a relighting method that is entirely data-driven, where intrinsics and lighting are each represented as latent variables. Our approach produces SOTA relightings of real scenes, as measured by standard metrics. We show that albedo can be recovered from our latent intrinsics without using any example albedos, and that the albedos recovered are competitive with SOTA methods.