# How to train your VAE

arXiv: https://arxiv.org/abs/2309.13160 · HTML: https://mlsanity.com/paper/2309.13160/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 22 Sep 2023.

## Builds on (most cited first, 16 of 16)

- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Precomputed Real-Time Texture Synthesis with Markovian Generative Adversarial Networks](https://mlsanity.com/paper/1604.04382/) (2016)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling](https://mlsanity.com/paper/1902.02102/) (2019)
- [Free-form Video Inpainting with 3D Gated Convolution and Temporal PatchGAN](https://mlsanity.com/paper/1904.10247/) (2019)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [Preventing Oversmoothing in VAE via Generalized Variance Parameterization](https://mlsanity.com/paper/2102.08663/) (2021)

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

- [Brain Latent Progression: Individual-based Spatiotemporal Disease Progression on 3D Brain MRIs via Latent Diffusion](https://mlsanity.com/paper/2502.08560/) (2025)
- [A Multi-Agent Framework Integrating Large Language Models and Generative AI for Accelerated Metamaterial Design](https://mlsanity.com/paper/2503.19889/) (2025)
- [FedGMI: Generative Model-Driven Federated Learning for Probabilistic Mixture Inference](https://mlsanity.com/paper/2605.08760/) (2026)

## Abstract (arXiv)

Variational Autoencoders (VAEs) have become a cornerstone in generative modeling and representation learning within machine learning. This paper explores a nuanced aspect of VAEs, focusing on interpreting the Kullback-Leibler (KL) Divergence, a critical component within the Evidence Lower Bound (ELBO) that governs the trade-off between reconstruction accuracy and regularization. Meanwhile, the KL Divergence enforces alignment between latent variable distributions and a prior imposing a structure on the overall latent space but leaves individual variable distributions unconstrained. The proposed method redefines the ELBO with a mixture of Gaussians for the posterior probability, introduces a regularization term to prevent variance collapse, and employs a PatchGAN discriminator to enhance texture realism. Implementation details involve ResNetV2 architectures for both the Encoder and Decoder. The experiments demonstrate the ability to generate realistic faces, offering a promising solution for enhancing VAE-based generative models.