We introduce a novel approach for generative 3D modeling that explicitly encourages the physical and thus functional consistency of the generated shapes. To this end, we advocate the use of online physical simulation as part of learning a generative model. Unlike previous related methods, our approach is trained end-to-end with a fully differentiable physical simulator in the training loop. We accomplish this by leveraging recent advances in differentiable programming, and introducing a fully differentiable pointbased physical simulation layer, which accurately evaluates the shape's stability when subjected to gravity. We then incorporate this layer in a signed distance function (SDF) shape decoder. By augmenting a conventional SDF decoder with our simulation layer, we demonstrate through extensive experiments that online physical simulation improves the accuracy, visual plausibility and physical validity of the resulting shapes, while requiring no additional data or annotation effort.