  Recent approaches build on implicit neural representations (INRs) to propose
generative models over function spaces. However, they are computationally
costly when dealing with inference tasks, such as missing data imputation, or
directly cannot tackle them. In this work, we propose a novel deep generative
model, named VAMoH. VAMoH combines the capabilities of modeling continuous
functions using INRs and the inference capabilities of Variational Autoencoders
(VAEs). In addition, VAMoH relies on a normalizing flow to define the prior,
and a mixture of hypernetworks to parametrize the data log-likelihood. This
gives VAMoH a high expressive capability and interpretability. Through
experiments on a diverse range of data types, such as images, voxels, and
climate data, we show that VAMoH can effectively learn rich distributions over
continuous functions. Furthermore, it can perform inference-related tasks, such
as conditional super-resolution generation and in-painting, as well or better
than previous approaches, while being less computationally demanding.
