State-of-the-art 3D-aware generative models rely on coordinate-based MLPs to parameterize 3D radiance fields. While demonstrating impressive results, querying an MLP for every sample along each ray leads to slow rendering.Therefore, existing approaches often render low-resolution feature maps and process them with an upsampling network to obtain the final image. Albeit efficient, neural rendering often entangles viewpoint and content such that changing the camera pose results in unwanted changes of geometry or appearance.Motivated by recent results in voxel-based novel view synthesis, we investigate the utility of sparse voxel grid representations for fast and 3D-consistent generative modeling in this paper.Our results demonstrate that monolithic MLPs can indeed be replaced by 3D convolutions when combining sparse voxel grids with progressive growing, free space pruning and appropriate regularization.To obtain a compact representation of the scene and allow for scaling to higher voxel resolutions, our model disentangles the foreground object (modeled in 3D) from the background (modeled in 2D).In contrast to existing approaches, our method requires only a single forward pass to generate a full 3D scene. It hence allows for efficient rendering from arbitrary viewpoints while yielding 3D consistent results with high visual fidelity. Code and models are available at https://github.com/autonomousvision/voxgraf.