We propose a neural formulation for estimating the appearance of complex luminaires. We focus on challenging luminaires with complex light transport (e.g., small emitters enclosed by multiple specular layers) that are difficult for (bidirectional) path tracing. To this end, we use light tracing to construct paths from emitters to the exit surfaces and formulate appearance estimation as a distribution learning problem. Specifically, we model the probability density function (pdf) of outgoing radiance on the exit surfaces using a large normalizing flow network, and recover the outgoing radiance as the product of the estimated pdf and flux. To enable efficient inference, we distill the learned appearance into a lightweight MLP that directly estimates radiance on the exit surfaces. We additionally train a sampling network for effective direct illumination computation from the luminaire, and a blending network to composite the luminaire into the scene. Our formulation makes it feasible to render challenging luminaires using low sample counts in arbitrary scenes.