# Variance Loss in Variational Autoencoders

arXiv: https://arxiv.org/abs/2002.09860 · HTML: https://mlsanity.com/paper/2002.09860/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [A survey on Variational Autoencoders from a GreenAI perspective](https://mlsanity.com/paper/2103.01071/) (2021)
- [Posterior Collapse as a Phase Transition in Variational Autoencoders](https://mlsanity.com/paper/2510.01621/) (2025)
- [Enhancing variational generation through self-decomposition](https://mlsanity.com/paper/2202.02738/) (2022)

## Abstract (arXiv)

In this article, we highlight what appears to be major issue of Variational Autoencoders, evinced from an extensive experimentation with different network architectures and datasets: the variance of generated data is significantly lower than that of training data. Since generative models are usually evaluated with metrics such as the Frechet Inception Distance (FID) that compare the distributions of (features of) real versus generated images, the variance loss typically results in degraded scores. This problem is particularly relevant in a two stage setting, where we use a second VAE to sample in the latent space of the first VAE. The minor variance creates a mismatch between the actual distribution of latent variables and those generated by the second VAE, that hinders the beneficial effects of the second stage. Renormalizing the output of the second VAE towards the expected normal spherical distribution, we obtain a sudden burst in the quality of generated samples, as also testified in terms of FID.