  Among likelihood-based approaches for deep generative modelling, variational
autoencoders (VAEs) offer scalable amortized posterior inference and fast
sampling. However, VAEs are also more and more outperformed by competing models
such as normalizing flows (NFs), deep-energy models, or the new denoising
diffusion probabilistic models (DDPMs). In this preliminary work, we improve
VAEs by demonstrating how DDPMs can be used for modelling the prior
distribution of the latent variables. The diffusion prior model improves upon
Gaussian priors of classical VAEs and is competitive with NF-based priors.
Finally, we hypothesize that hierarchical VAEs could similarly benefit from the
enhanced capacity of diffusion priors.
