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Perceptual metrics, like the Fr\'echet Inception Distance (FID), are widelyused to assess the similarity between synthetically generated and ground truth(real) images. The key idea behind these metrics is to compute errors in a deepfeature space that captures perceptually and semantically rich image features.Despite their popularity, the effect that different deep features and theirdesign choices have on a perceptual metric has not been well studied. In thiswork, we perform a causal analysis linking differences in semantic attributesand distortions between face image distributions to Fr\'echet distances (FD)using several popular deep feature spaces. A key component of our analysis isthe creation of synthetic counterfactual faces using deep face generators. Ourexperiments show that the FD is heavily influenced by its feature space'straining dataset and objective function. For example, FD using featuresextracted from ImageNet-trained models heavily emphasize hats over regions likethe eyes and mouth. Moreover, FD using features from a face gender classifieremphasize hair length more than distances in an identity (recognition) featurespace. Finally, we evaluate several popular face generation models acrossfeature spaces and find that StyleGAN2 consistently ranks higher than otherface generators, except with respect to identity (recognition) features. Thissuggests the need for considering multiple feature spaces when evaluatinggenerative models and using feature spaces that are tuned to nuances of thedomain of interest.

F?D: On understanding the role of deep feature spaces on face generation evaluation