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.
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