# Improving Variational Auto-Encoders using Householder Flow

arXiv: https://arxiv.org/abs/1611.09630 · HTML: https://mlsanity.com/paper/1611.09630/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2016.

## Built on by (most cited first, 30 of 42)

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- [Cauchy-Schwarz Regularized Autoencoder](https://mlsanity.com/paper/2101.02149/) (2021)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Variational Laplace Autoencoders](https://mlsanity.com/paper/2211.17267/) (2022)
- [VAST: Vivify Your Talking Avatar via Zero-Shot Expressive Facial Style Transfer](https://mlsanity.com/paper/2308.04830/) (2023)
- [Bidirectional Normalizing Flow: From Data to Noise and Back](https://mlsanity.com/paper/2512.10953/) (2025)
- [Reducing the Amortization Gap in Variational Autoencoders: A Bayesian Random Function Approach](https://mlsanity.com/paper/2102.03151/) (2021)
- [Review of end-to-end speech synthesis technology based on deep learning](https://mlsanity.com/paper/2104.09995/) (2021)
- [Training Energy-Based Normalizing Flow with Score-Matching Objectives](https://mlsanity.com/paper/2305.15267/) (2023)
- [A Conditional Flow Variational Autoencoder for Controllable Synthesis of Virtual Populations of Anatomy](https://mlsanity.com/paper/2306.14680/) (2023)
- [Flowification: Everything is a Normalizing Flow](https://mlsanity.com/paper/2205.15209/) (2022)
- [Unify and Conquer: How Phonetic Feature Representation Affects Polyglot Text-To-Speech (TTS)](https://mlsanity.com/paper/2207.01547/) (2022)
- [Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry](https://mlsanity.com/paper/2505.08087/) (2025)
- [Variational Inference with Locally Enhanced Bounds for Hierarchical Models](https://mlsanity.com/paper/2203.04432/) (2022)
- [Mix and Match: An Empirical Study on Training Corpus Composition for Polyglot Text-To-Speech (TTS)](https://mlsanity.com/paper/2207.01507/) (2022)
- [Constructive approximate transport maps with normalizing flows](https://mlsanity.com/paper/2412.19366/) (2024)
- [Modeling Item Response Theory with Stochastic Variational Inference](https://mlsanity.com/paper/2108.11579/) (2021)
- [A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks](https://mlsanity.com/paper/2303.02637/) (2023)
- [Learning and Generalization in Overparameterized Normalizing Flows](https://mlsanity.com/paper/2106.10535/) (2021)
- [Viscos Flows: Variational Schur Conditional Sampling With Normalizing Flows](https://mlsanity.com/paper/2107.02474/) (2021)
- [VFDS: Variational Foresight Dynamic Selection in Bayesian Neural Networks for Efficient Human Activity Recognition](https://mlsanity.com/paper/2204.00130/) (2022)
- [Latent Variable Modelling Using Variational Autoencoders: A survey](https://mlsanity.com/paper/2206.09891/) (2022)
- [Sparse Representation Learning with Modified q-VAE towards Minimal Realization of World Model](https://mlsanity.com/paper/2208.03936/) (2022)
- [An Overview on Controllable Text Generation via Variational Auto-Encoders](https://mlsanity.com/paper/2211.07954/) (2022)
- [A Novel Application of Conditional Normalizing Flows: Stellar Age Inference with Gyrochronology](https://mlsanity.com/paper/2307.08753/) (2023)
- [Physics-integrated generative modeling using attentive planar normalizing flow based variational autoencoder](https://mlsanity.com/paper/2404.12267/) (2024)

## Abstract (arXiv)

Variational auto-encoders (VAE) are scalable and powerful generative models. However, the choice of the variational posterior determines tractability and flexibility of the VAE. Commonly, latent variables are modeled using the normal distribution with a diagonal covariance matrix. This results in computational efficiency but typically it is not flexible enough to match the true posterior distribution. One fashion of enriching the variational posterior distribution is application of normalizing flows, i.e., a series of invertible transformations to latent variables with a simple posterior. In this paper, we follow this line of thinking and propose a volume-preserving flow that uses a series of Householder transformations. We show empirically on MNIST dataset and histopathology data that the proposed flow allows to obtain more flexible variational posterior and competitive results comparing to other normalizing flows.