# Beyond Vanilla Variational Autoencoders: Detecting Posterior Collapse in Conditional and Hierarchical Variational Autoencoders

arXiv: https://arxiv.org/abs/2306.05023 · HTML: https://mlsanity.com/paper/2306.05023/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 50 references that are in the map.
- First posted on arXiv 8 Jun 2023.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Neural Variational Inference for Text Processing](https://mlsanity.com/paper/1511.06038/) (2015)
- [Identity Matters in Deep Learning](https://mlsanity.com/paper/1611.04231/) (2016)
- [BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling](https://mlsanity.com/paper/1902.02102/) (2019)
- [Generating Sentences by Editing Prototypes](https://mlsanity.com/paper/1709.08878/) (2017)
- [An Uncertain Future: Forecasting from Static Images using Variational Autoencoders](https://mlsanity.com/paper/1606.07873/) (2016)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Variational Autoencoders Pursue PCA Directions (by Accident)](https://mlsanity.com/paper/1812.06775/) (2018)
- [Improved Variational Autoencoders for Text Modeling using Dilated Convolutions](https://mlsanity.com/paper/1702.08139/) (2017)
- [PixelVAE: A Latent Variable Model for Natural Images](https://mlsanity.com/paper/1611.05013/) (2016)
- [Deep linear neural networks with arbitrary loss: All local minima are global](https://mlsanity.com/paper/1712.01473/) (2017)

## Built on by (most cited first, 7 of 7)

- [Plasma State Monitoring and Disruption Characterization using Multimodal VAEs](https://mlsanity.com/paper/2504.17710/) (2025)
- [Variational Rank Reduction Autoencoders](https://mlsanity.com/paper/2505.09458/) (2025)
- [Transferring disentangled representations: bridging the gap between synthetic and real images](https://mlsanity.com/paper/2409.18017/) (2024)
- [Lost and Found in Translation: Variational Diagnostics for Neural Codebook Channels](https://mlsanity.com/paper/2605.18846/) (2026)
- [FL-CLEANER: byzantine and backdoor defense by CLustering Errors of Activation maps in Non-iid fedErated leaRning](https://mlsanity.com/paper/2501.12123/) (2025)
- [RST: certifying and constructing prescribed information in variational autoencoders](https://mlsanity.com/paper/2605.18224/) (2026)
- [Perfect Reconstruction Cannot Show Whether Two Codebooks on a VAE's Latent Space Agree](https://mlsanity.com/paper/2610.14012/) (2026)

## Abstract (arXiv)

The posterior collapse phenomenon in variational autoencoder (VAE), where the variational posterior distribution closely matches the prior distribution, can hinder the quality of the learned latent variables. As a consequence of posterior collapse, the latent variables extracted by the encoder in VAE preserve less information from the input data and thus fail to produce meaningful representations as input to the reconstruction process in the decoder. While this phenomenon has been an actively addressed topic related to VAE performance, the theory for posterior collapse remains underdeveloped, especially beyond the standard VAE. In this work, we advance the theoretical understanding of posterior collapse to two important and prevalent yet less studied classes of VAE: conditional VAE and hierarchical VAE. Specifically, via a non-trivial theoretical analysis of linear conditional VAE and hierarchical VAE with two levels of latent, we prove that the cause of posterior collapses in these models includes the correlation between the input and output of the conditional VAE and the effect of learnable encoder variance in the hierarchical VAE. We empirically validate our theoretical findings for linear conditional and hierarchical VAE and demonstrate that these results are also predictive for non-linear cases with extensive experiments.