Recovering the high dynamic range of a natural scene from a single low dynamic range image is an important task with many applications in photography, image editing, and photo-realistic rendering. The wide range of naturally occurring illumination conditions makes their reconstruction from clipped and compressed RGB values challenging. We present a novel approach for single-image HDR reconstruction in the intrinsic domain. By decomposing the image into diffuse reflectance and illumination layers, we can divide the reconstruction problem into two simpler subtasks that we address individually. Our approach generates faithful illumination levels by learning to reconstruct HDR shading as well as recovering clipped color information by separately reconstructing the albedo.