Fréchet inception distance
The Fréchet inception distance (FID) is a metric used to assess the quality of images created by a generative model, like a generative adversarial network (GAN). Unlike the earlier inception score (IS), which evaluates only the distribution of generated images, the FID compares the distribution of generated images with the distribution of real images that were used to train the generator.
The FID metric is the squared Wasserstein metric between two multidimensional Gaussian distributions: , the distribution of some neural network internal representations (activations) of the images generated by the model and the distribution of the same neural network activations from the "world" of real images used to train the model. As a neural network the Inception v3 trained on the ImageNet is commonly used. As a result, it can be computed from the mean and the covariance of the activations when the synthesized and real images are fed into the Inception network as: 
Rather than directly comparing images pixel by pixel (for example, as done by the L2 norm), the FID compares the mean and standard deviation of one of the deeper layers in a convolutional neural network named Inception v3. These layers are closer to output nodes that correspond to real-world objects such as a specific breed of dog or an airplane, and further from the shallow layers near the input image. As a result, they tend to mimic human perception of similarity in images.
The FID metric is the current standard metric for assessing the quality of generative models as of 2020. It has been used to measure the quality of many recent models including the high-resolution StyleGAN1 and StyleGAN2 networks.
Specialized variants of FID have been suggested as evaluation metric for music enhancement algorithms as Fréchet Audio Distance (FAD), for generative models of video as Fréchet Video Distance (FVD),[unreliable source?] and for AI-generated molecules as Fréchet ChemNet Distance (FCD).
Chong and Forsyth  showed FID to be statistically biased, in the sense that their expected value over a finite data is not their true value. Also, because FID measured the Wasserstein distance towards the ground-truth distribution, it is inadequate for evaluating the quality of generators in domain adaptation setups, or in zero-shot generation. Finally, while FID is more consistent with human judgement than previously used inception score, there are cases where FID is inconsistent with human judgment (e.g. Figure 3,5 in Liu et al.).
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