# Matching aggregate posteriors in the variational autoencoder

arXiv: https://arxiv.org/abs/2311.07693 · HTML: https://mlsanity.com/paper/2311.07693/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 94 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 30 of 59)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)

## Built on by (most cited first, 6 of 6)

- [ARD-VAE: A Statistical Formulation to Find the Relevant Latent Dimensions of Variational Autoencoders](https://mlsanity.com/paper/2501.10901/) (2025)
- [On Kernel-based Variational Autoencoder](https://mlsanity.com/paper/2405.12783/) (2024)
- [Analyzing Multimodal Integration in the Variational Autoencoder from an Information-Theoretic Perspective](https://mlsanity.com/paper/2411.00522/) (2024)
- [Disentanglement Analysis in Deep Latent Variable Models Matching Aggregate Posterior Distributions](https://mlsanity.com/paper/2501.15705/) (2025)
- [AdaSemSeg: An Adaptive Few-shot Semantic Segmentation of Seismic Facies](https://mlsanity.com/paper/2501.16760/) (2025)
- [Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage](https://mlsanity.com/paper/2605.12764/) (2026)

## Abstract (arXiv)

The variational autoencoder (VAE) is a well-studied, deep, latent-variable model (DLVM) that efficiently optimizes the variational lower bound of the log marginal data likelihood and has a strong theoretical foundation. However, the VAE's known failure to match the aggregate posterior often results in pockets/holes in the latent distribution (i.e., a failure to match the prior) and/or posterior collapse, which is associated with a loss of information in the latent space. This paper addresses these shortcomings in VAEs by reformulating the objective function associated with VAEs in order to match the aggregate/marginal posterior distribution to the prior. We use kernel density estimate (KDE) to model the aggregate posterior in high dimensions. The proposed method is named the aggregate variational autoencoder (AVAE) and is built on the theoretical framework of the VAE. Empirical evaluation of the proposed method on multiple benchmark data sets demonstrates the effectiveness of the AVAE relative to state-of-the-art (SOTA) methods.