# Distribution Matching in Variational Inference

arXiv: https://arxiv.org/abs/1802.06847 · HTML: https://mlsanity.com/paper/1802.06847/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2018.

## Built on by (most cited first, 30 of 35)

- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [D2C: Diffusion-Denoising Models for Few-shot Conditional Generation](https://mlsanity.com/paper/2106.06819/) (2021)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [Distribution-Aware Testing of Neural Networks Using Generative Models](https://mlsanity.com/paper/2102.13602/) (2021)
- [A survey on Variational Autoencoders from a GreenAI perspective](https://mlsanity.com/paper/2103.01071/) (2021)
- [Calibration by Distribution Matching: Trainable Kernel Calibration Metrics](https://mlsanity.com/paper/2310.20211/) (2023)
- [VCT: Training Consistency Models with Variational Noise Coupling](https://mlsanity.com/paper/2502.18197/) (2025)
- [Bottlenecks CLUB: Unifying Information-Theoretic Trade-offs Among Complexity, Leakage, and Utility](https://mlsanity.com/paper/2207.04895/) (2022)
- [Comparing the latent space of generative models](https://mlsanity.com/paper/2207.06812/) (2022)
- [FrePolad: Frequency-Rectified Point Latent Diffusion for Point Cloud Generation](https://mlsanity.com/paper/2311.12090/) (2023)
- [Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation](https://mlsanity.com/paper/2106.10591/) (2021)
- [Variational Leakage: The Role of Information Complexity in Privacy Leakage](https://mlsanity.com/paper/2106.02818/) (2021)
- [Latent Space Diffusion Models of Cryo-EM Structures](https://mlsanity.com/paper/2211.14169/) (2022)
- [Matching aggregate posteriors in the variational autoencoder](https://mlsanity.com/paper/2311.07693/) (2023)
- [Learning Latent Space Hierarchical EBM Diffusion Models](https://mlsanity.com/paper/2405.13910/) (2024)
- [ARD-VAE: A Statistical Formulation to Find the Relevant Latent Dimensions of Variational Autoencoders](https://mlsanity.com/paper/2501.10901/) (2025)
- [From latent dynamics to meaningful representations](https://mlsanity.com/paper/2209.00905/) (2022)
- [Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectives](https://mlsanity.com/paper/2309.00380/) (2023)
- [Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generation](https://mlsanity.com/paper/2607.27372/) (2026)
- [Bayesian Distributional Policy Gradients](https://mlsanity.com/paper/2103.11265/) (2021)
- [Probabilistic Autoencoder using Fisher Information](https://mlsanity.com/paper/2110.14947/) (2021)
- [CoVAE: Consistency Training of Variational Autoencoders](https://mlsanity.com/paper/2507.09103/) (2025)
- [Disentanglement Analysis in Deep Latent Variable Models Matching Aggregate Posterior Distributions](https://mlsanity.com/paper/2501.15705/) (2025)
- [Quartet of Diffusions: Structure-Aware Point Cloud Generation through Part and Symmetry Guidance](https://mlsanity.com/paper/2601.20425/) (2026)
- [Deep Dive into Semi-Supervised ELBO for Improving Classification Performance](https://mlsanity.com/paper/2108.12734/) (2021)
- [RENs: Relevance Encoding Networks](https://mlsanity.com/paper/2205.13061/) (2022)
- [Learning variational autoencoders via MCMC speed measures](https://mlsanity.com/paper/2308.13731/) (2023)
- [On Unsupervised Image-to-image translation and GAN stability](https://mlsanity.com/paper/2403.09646/) (2023)
- [Resultant: Incremental Effectiveness on Likelihood for Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/2409.03801/) (2024)

## Abstract (arXiv)

With the increasingly widespread deployment of generative models, there is a mounting need for a deeper understanding of their behaviors and limitations. In this paper, we expose the limitations of Variational Autoencoders (VAEs), which consistently fail to learn marginal distributions in both latent and visible spaces. We show this to be a consequence of learning by matching conditional distributions, and the limitations of explicit model and posterior distributions. It is popular to consider Generative Adversarial Networks (GANs) as a means of overcoming these limitations, leading to hybrids of VAEs and GANs. We perform a large-scale evaluation of several VAE-GAN hybrids and analyze the implications of class probability estimation for learning distributions. While promising, we conclude that at present, VAE-GAN hybrids have limited applicability: they are harder to scale, evaluate, and use for inference compared to VAEs; and they do not improve over the generation quality of GANs.