Creative processes of artists often start with hand-drawn sketches illustrating an object. Pre-visualizing these keyframes is especially challenging when applied to volumetric materials such as smoke. The authored 3D density volumes must capture realistic flow details and turbulent structures, which is highly non-trivial and remains a manual and time-consuming process. We therefore present a method to compute a 3D smoke density field directly from 2D artist sketches, bridging the gap between early-stage prototyping of smoke keyframes and pre-visualization. From the sketch inputs, we compute an initial volume estimate and optimize the density iteratively with an updater CNN. Our differentiable sketcher is embedded into the end-to-end training, which results in robust reconstructions. Our training data set and sketch augmentation strategy are designed such that it enables general applicability. We evaluate the method on synthetic inputs and sketches from artists depicting both realistic smoke volumes and highly non-physical smoke shapes. The high computational performance and robustness of our method at test time allows interactive authoring sessions of volumetric density fields for rapid prototyping of ideas by novice users.