We present an approach to infer a layer-structured 3D representation of a scene from a single input image. This allows us to infer not only the depth of the visible pixels, but also to capture the texture and depth for content in the scene that is not directly visible. We overcome the challenge posed by the lack of direct supervision by instead leveraging a more naturally available multi-view supervisory signal. Our insight is to use view synthesis as a proxy task: we enforce that our representation (inferred from a single image), when rendered from a novel perspective, matches the true observed image. We present a learning framework that operationalizes this insight using a new, differentiable novel view renderer. We provide qualitative and quantitative validation of our approach in two different settings, and demonstrate that we can learn to capture the hidden aspects of a scene.