# On GANs and GMMs

arXiv: https://arxiv.org/abs/1805.12462 · HTML: https://mlsanity.com/paper/1805.12462/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2018.

## Built on by (most cited first, 30 of 62)

- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [ProDiff: Progressive Fast Diffusion Model For High-Quality Text-to-Speech](https://mlsanity.com/paper/2207.06389/) (2022)
- [Generating images of rare concepts using pre-trained diffusion models](https://mlsanity.com/paper/2304.14530/) (2023)
- [LAformer: Trajectory Prediction for Autonomous Driving with Lane-Aware Scene Constraints](https://mlsanity.com/paper/2302.13933/) (2023)
- [Norm-guided latent space exploration for text-to-image generation](https://mlsanity.com/paper/2306.08687/) (2023)
- [DivCo: Diverse Conditional Image Synthesis via Contrastive Generative Adversarial Network](https://mlsanity.com/paper/2103.07893/) (2021)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [GATraj: A Graph- and Attention-based Multi-Agent Trajectory Prediction Model](https://mlsanity.com/paper/2209.07857/) (2022)
- [Conditional Sound Generation Using Neural Discrete Time-Frequency Representation Learning](https://mlsanity.com/paper/2107.09998/) (2021)
- [FoleyGAN: Visually Guided Generative Adversarial Network-Based Synchronous Sound Generation in Silent Videos](https://mlsanity.com/paper/2107.09262/) (2021)
- [AGTGAN: Unpaired Image Translation for Photographic Ancient Character Generation](https://mlsanity.com/paper/2303.07012/) (2023)
- [Evaluating generative audio systems and their metrics](https://mlsanity.com/paper/2209.00130/) (2022)
- [On Learning the Transformer Kernel](https://mlsanity.com/paper/2110.08323/) (2021)
- [Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2205.15784/) (2022)
- [MCL-GAN: Generative Adversarial Networks with Multiple Specialized Discriminators](https://mlsanity.com/paper/2107.07260/) (2021)
- [Survey on the Evaluation of Generative Models in Music](https://mlsanity.com/paper/2506.05104/) (2025)
- [Data-Copying in Generative Models: A Formal Framework](https://mlsanity.com/paper/2302.13181/) (2023)
- [Model Extraction and Defenses on Generative Adversarial Networks](https://mlsanity.com/paper/2101.02069/) (2021)
- [Adversarial robustness for latent models: Revisiting the robust-standard accuracies tradeoff](https://mlsanity.com/paper/2110.11950/) (2021)
- [Semantic Contextualization of Face Forgery: A New Definition, Dataset, and Detection Method](https://mlsanity.com/paper/2405.08487/) (2024)
- [Scenario generation for market risk models using generative neural networks](https://mlsanity.com/paper/2109.10072/) (2021)
- [Instability and Local Minima in GAN Training with Kernel Discriminators](https://mlsanity.com/paper/2208.09938/) (2022)
- [Continual Learning with Fully Probabilistic Models](https://mlsanity.com/paper/2104.09240/) (2021)
- [A Realism Metric for Generated LiDAR Point Clouds](https://mlsanity.com/paper/2208.14958/) (2022)
- [Image Modeling with Deep Convolutional Gaussian Mixture Models](https://mlsanity.com/paper/2104.12686/) (2021)
- [MisConv: Convolutional Neural Networks for Missing Data](https://mlsanity.com/paper/2110.14010/) (2021)
- [Aggregating Layers for Deepfake Detection](https://mlsanity.com/paper/2210.05478/) (2022)
- [SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics](https://mlsanity.com/paper/2302.03663/) (2023)
- [Privacy Measurement in Tabular Synthetic Data: State of the Art and Future Research Directions](https://mlsanity.com/paper/2311.17453/) (2023)
- [On the Effectiveness of Acoustic BPE in Decoder-Only TTS](https://mlsanity.com/paper/2407.03892/) (2024)

## Abstract (arXiv)

A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in particular have shown the ability to generate remarkably realistic high resolution sampled images. At the same time, many authors have pointed out that GANs may fail to model the full distribution ("mode collapse") and that using the learned models for anything other than generating samples may be very difficult. In this paper, we examine the utility of GANs in learning statistical models of images by comparing them to perhaps the simplest statistical model, the Gaussian Mixture Model. First, we present a simple method to evaluate generative models based on relative proportions of samples that fall into predetermined bins. Unlike previous automatic methods for evaluating models, our method does not rely on an additional neural network nor does it require approximating intractable computations. Second, we compare the performance of GANs to GMMs trained on the same datasets. While GMMs have previously been shown to be successful in modeling small patches of images, we show how to train them on full sized images despite the high dimensionality. Our results show that GMMs can generate realistic samples (although less sharp than those of GANs) but also capture the full distribution, which GANs fail to do. Furthermore, GMMs allow efficient inference and explicit representation of the underlying statistical structure. Finally, we discuss how GMMs can be used to generate sharp images.