We develop ProxelGen, a protein structure generative model that operates on 3D densities as opposed to the prevailing 3D point cloud representations. Representing proteins as voxelized densities, or proxels, enables new tasks and conditioning capabilities. We generate proteins encoded as proxels via a 3D CNN-based VAE in conjunction with a diffusion model operating on its latent space. Compared to state-of-the-art models, ProxelGen's samples achieve higher novelty, better FID scores, and the same level of designability as the training set. ProxelGen's advantages are demonstrated in a standard motif scaffolding benchmark, and we show how 3D density-based generation allows for more flexible shape conditioning.