Diffusion-based methods have shown impressive visual results in the text-to-image domain. They first learn a latent space using an autoencoder, then run a denoising process on the bottleneck to generate new samples. However, learning an autoencoder requires substantial data in the target domain. Such data is scarce for 3D generation, prohibiting the learning of large-scale diffusion models for 3D synthesis. We present a novel approach to the generation of static and articulated 3D assets that has a 3D autodecoder at its core. The 3D autodecoder framework embeds properties learned from the target dataset in the latent space, which can then be decoded into a volumetric representation for rendering view-consistent appearance and geometry. We then identify the appropriate intermediate volumetric latent space, and introduce robust normalization and de-normalization operations to learn a 3D diffusion from 2D images or monocular videos of rigid or articulated objects. Our approach is flexible enough to use either existing camera supervision or no camera information at all -- instead efficiently learning it during training. Our evaluations demonstrate that our generation results outperform state-of-the-art alternatives on various benchmark datasets and metrics, including multi-view image datasets of synthetic objects, real in-the-wild videos of moving people, and a large-scale, real video dataset of static objects.