  We investigate the problem of producing diverse solutions to an image
super-resolution problem. From a probabilistic perspective, this can be done by
sampling from the posterior distribution of an inverse problem, which requires
the definition of a prior distribution on the high-resolution images. In this
work, we propose to use a pretrained hierarchical variational autoencoder
(HVAE) as a prior. We train a lightweight stochastic encoder to encode
low-resolution images in the latent space of a pretrained HVAE. At inference,
we combine the low-resolution encoder and the pretrained generative model to
super-resolve an image. We demonstrate on the task of face super-resolution
that our method provides an advantageous trade-off between the computational
efficiency of conditional normalizing flows techniques and the sample quality
of diffusion based methods.
