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 \textit{proxels}, enables new tasks, conditioning capabilities, and a straightforward path for employing convolutional model architectures with different inductive biases than previous generative models. 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 and better FID scores while maintaining designability of 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.