# Posterior Collapse as a Phase Transition in Variational Autoencoders

arXiv: https://arxiv.org/abs/2510.01621 · HTML: https://mlsanity.com/paper/2510.01621/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 20 of 20)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [IntroVAE: Introspective Variational Autoencoders for Photographic Image Synthesis](https://mlsanity.com/paper/1807.06358/) (2018)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [Variational Autoencoders Pursue PCA Directions (by Accident)](https://mlsanity.com/paper/1812.06775/) (2018)
- [PixelVAE: A Latent Variable Model for Natural Images](https://mlsanity.com/paper/1611.05013/) (2016)
- [The Usual Suspects? Reassessing Blame for VAE Posterior Collapse](https://mlsanity.com/paper/1912.10702/) (2019)
- [Loss Landscapes of Regularized Linear Autoencoders](https://mlsanity.com/paper/1901.08168/) (2019)
- [Improving Explorability in Variational Inference with Annealed Variational Objectives](https://mlsanity.com/paper/1809.01818/) (2018)
- [Posterior Collapse of a Linear Latent Variable Model](https://mlsanity.com/paper/2205.04009/) (2022)
- [Quantitative Understanding of VAE as a Non-linearly Scaled Isometric Embedding](https://mlsanity.com/paper/2007.15190/) (2020)
- [High-dimensional Asymptotics of VAEs: Threshold of Posterior Collapse and Dataset-Size Dependence of Rate-Distortion Curve](https://mlsanity.com/paper/2309.07663/) (2023)
- [Variance Loss in Variational Autoencoders](https://mlsanity.com/paper/2002.09860/) (2020)

## Built on by (most cited first, 4 of 4)

- [Latent Spectroscopy: Posterior Collapse as a Feature](https://mlsanity.com/paper/2605.22691/) (2026)
- [We Need a More Robust Classifier: Dual Causal Learning Empowers Domain-Incremental Time Series Classification](https://mlsanity.com/paper/2601.10312/) (2026)
- [Spherical VAE with Cluster-Aware Feasible Regions: Guaranteed Prevention of Posterior Collapse](https://mlsanity.com/paper/2603.10935/) (2026)
- [RST: certifying and constructing prescribed information in variational autoencoders](https://mlsanity.com/paper/2605.18224/) (2026)

## Abstract (arXiv)

We investigate the phenomenon of posterior collapse in variational autoencoders (VAEs) from the perspective of statistical physics, and reveal that it constitutes a phase transition governed jointly by data structure and model hyper-parameters. By analyzing the stability of the trivial solution associated with posterior collapse, we identify a critical hyper-parameter threshold. In particular, we derive an explicit criterion for the onset of collapse: posterior collapse occurs when the decoder variance exceeds the largest eigenvalue of the data covariance matrix. This critical boundary, separating meaningful latent inference from collapse, is characterized by a discontinuity in the KL divergence between the approximate posterior and the prior distribution, where the KL divergence and its derivatives exhibit clear non-analytic behavior. We validate this critical behavior on both synthetic and real-world datasets, confirming the existence of a phase transition. The experimental results align well with our theoretical predictions, demonstrating the robustness of our collapse criterion across various VAE architectures. Our stability-based analysis demonstrate that posterior collapse is not merely an optimization failure, but rather an emerging phase transition arising from the interplay between data structure and variational constraints. This perspective offers new insights into the trainability and representational capacity of deep generative models.