The variational autoencoder (VAE) model with KL loss was introduced in [Auto-Encoding Variational Bayes](https://arxiv.org/abs/1312.6114v11) by Diederik P. Kingma and Max Welling. The model is used in 🤗 Diffusers to encode images into latents and to decode latent representations into images.  
The abstract from the paper is: