# Evaluating generative networks using Gaussian mixtures of image features

arXiv: https://arxiv.org/abs/2110.05240 · HTML: https://mlsanity.com/paper/2110.05240/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 8 Oct 2021.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [PIPAL: a Large-Scale Image Quality Assessment Dataset for Perceptual Image Restoration](https://mlsanity.com/paper/2007.12142/) (2020)
- [Effectively Unbiased FID and Inception Score and where to find them](https://mlsanity.com/paper/1911.07023/) (2019)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Optimal transport for Gaussian mixture models](https://mlsanity.com/paper/1710.07876/) (2017)
- [An Improved Evaluation Framework for Generative Adversarial Networks](https://mlsanity.com/paper/1803.07474/) (2018)
- [Conditional Frechet Inception Distance](https://mlsanity.com/paper/2103.11521/) (2021)
- [A Distance for HMMs based on Aggregated Wasserstein Metric and State Registration](https://mlsanity.com/paper/1608.01747/) (2016)

## Built on by (most cited first, 11 of 11)

- [Geometry Fidelity for Spherical Images](https://mlsanity.com/paper/2407.18207/) (2024)
- [A Pragmatic Note on Evaluating Generative Models with Fr'echet Inception Distance for Retinal Image Synthesis](https://mlsanity.com/paper/2502.17160/) (2025)
- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Space](https://mlsanity.com/paper/2310.11256/) (2023)
- [Unifying and extending Precision Recall metrics for assessing generative models](https://mlsanity.com/paper/2405.01611/) (2024)
- [Offline Evaluation of Set-Based Text-to-Image Generation](https://mlsanity.com/paper/2410.17331/) (2024)
- [Using Skew to Assess the Quality of GAN-generated Image Features](https://mlsanity.com/paper/2310.20636/) (2023)
- [Distribution-aware Noisy-label Crack Segmentation](https://mlsanity.com/paper/2410.09409/) (2024)
- [Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport](https://mlsanity.com/paper/2509.02109/) (2025)
- [A New Perspective on Precision and Recall for Generative Models](https://mlsanity.com/paper/2511.02414/) (2025)
- [What FID Hides: Detecting, Ranking, and Diagnosing Deviations in Generative Evaluation](https://mlsanity.com/paper/2608.24881/) (2026)

## Abstract (arXiv)

We develop a measure for evaluating the performance of generative networks given two sets of images. A popular performance measure currently used to do this is the Fr'echet Inception Distance (FID). FID assumes that images featurized using the penultimate layer of Inception-v3 follow a Gaussian distribution, an assumption which cannot be violated if we wish to use FID as a metric. However, we show that Inception-v3 features of the ImageNet dataset are not Gaussian; in particular, every single marginal is not Gaussian. To remedy this problem, we model the featurized images using Gaussian mixture models (GMMs) and compute the 2-Wasserstein distance restricted to GMMs. We define a performance measure, which we call WaM, on two sets of images by using Inception-v3 (or another classifier) to featurize the images, estimate two GMMs, and use the restricted 2-Wasserstein distance to compare the GMMs. We experimentally show the advantages of WaM over FID, including how FID is more sensitive than WaM to imperceptible image perturbations. By modelling the non-Gaussian features obtained from Inception-v3 as GMMs and using a GMM metric, we can more accurately evaluate generative network performance.