This disclosure relates to methods, non-transitory computer readable media, and systems that can render a virtual object in a digital image by using a source-specific-lighting-estimation-neural network to generate three-dimensional (“3D”) lighting parameters specific to a light source illuminating the digital image. To generate such source-specific-lighting parameters, for instance, the disclosed systems utilize a compact source-specific-lighting-estimation-neural network comprising both common network layers and network layers specific to different lighting parameters. In some embodiments, the disclosed systems further train such a source-specific-lighting-estimation-neural network to accurately estimate spatially varying lighting in a digital image based on comparisons of predicted environment maps from a differentiable-projection layer with ground-truth-environment maps.