  Recent advances have shown that GP priors, or their finite realisations, can
be encoded using deep generative models such as variational autoencoders
(VAEs). These learned generators can serve as drop-in replacements for the
original priors during MCMC inference. While this approach enables efficient
inference, it loses information about the hyperparameters of the original
models, and consequently makes inference over hyperparameters impossible and
the learned priors indistinct. To overcome this limitation, we condition the
VAE on stochastic process hyperparameters. This allows the joint encoding of
hyperparameters with GP realizations and their subsequent estimation during
inference. Further, we demonstrate that our proposed method, PriorCVAE, is
agnostic to the nature of the models which it approximates, and can be used,
for instance, to encode solutions of ODEs. It provides a practical tool for
approximate inference and shows potential in real-life spatial and
spatiotemporal applications.
