# Controlling Posterior Collapse by an Inverse Lipschitz Constraint on the Decoder Network

arXiv: https://arxiv.org/abs/2304.12770 · HTML: https://mlsanity.com/paper/2304.12770/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 55 references that are in the map.
- First posted on arXiv 25 Apr 2023.

## Builds on (most cited first, 30 of 33)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Semi-Amortized Variational Autoencoders](https://mlsanity.com/paper/1802.02550/) (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)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [The Usual Suspects? Reassessing Blame for VAE Posterior Collapse](https://mlsanity.com/paper/1912.10702/) (2019)
- [Avoiding Latent Variable Collapse With Generative Skip Models](https://mlsanity.com/paper/1807.04863/) (2018)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Unsupervised Discrete Sentence Representation Learning for Interpretable Neural Dialog Generation](https://mlsanity.com/paper/1804.08069/) (2018)
- [A Surprisingly Effective Fix for Deep Latent Variable Modeling of Text](https://mlsanity.com/paper/1909.00868/) (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)
- [Tackling Over-pruning in Variational Autoencoders](https://mlsanity.com/paper/1706.03643/) (2017)
- [Certifiably Robust Variational Autoencoders](https://mlsanity.com/paper/2102.07559/) (2021)
- [Variational approximations using Fisher divergence](https://mlsanity.com/paper/1905.05284/) (2019)
- [Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach](https://mlsanity.com/paper/1809.09505/) (2018)

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

- [Beyond Vanilla Variational Autoencoders: Detecting Posterior Collapse in Conditional and Hierarchical Variational Autoencoders](https://mlsanity.com/paper/2306.05023/) (2023)
- [A Controllable Appearance Representation for Flexible Transfer and Editing](https://mlsanity.com/paper/2504.15028/) (2025)
- [S2WTM: Spherical Sliced-Wasserstein Autoencoder for Topic Modeling](https://mlsanity.com/paper/2507.12451/) (2025)
- [Toward Architecture-Agnostic Local Control of Posterior Collapse in VAEs](https://mlsanity.com/paper/2508.12530/) (2025)
- [Quasi Monte Carlo methods enable extremely low-dimensional deep generative models](https://mlsanity.com/paper/2601.18676/) (2026)
- [Robust Provably Secure Image Steganography via Latent Iterative Optimization](https://mlsanity.com/paper/2603.09348/) (2026)
- [RST: certifying and constructing prescribed information in variational autoencoders](https://mlsanity.com/paper/2605.18224/) (2026)

## Abstract (arXiv)

Variational autoencoders (VAEs) are one of the deep generative models that have experienced enormous success over the past decades. However, in practice, they suffer from a problem called posterior collapse, which occurs when the encoder coincides, or collapses, with the prior taking no information from the latent structure of the input data into consideration. In this work, we introduce an inverse Lipschitz neural network into the decoder and, based on this architecture, provide a new method that can control in a simple and clear manner the degree of posterior collapse for a wide range of VAE models equipped with a concrete theoretical guarantee. We also illustrate the effectiveness of our method through several numerical experiments.