The Fréchet inception distance

To overcome the various shortcomings of the inception Score, the Fréchlet Inception Distance (FID) was proposed by Martin Heusel and others in their paper, GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium (https://arxiv.org/pdf/1706.08500.pdf). 

The equation to calculate the FID score is as follows:

The preceding equation represents the FID score between the real images, x, and the generated images, g. To calculate the FID score, we use the Inception network to extract the feature maps from an intermediate layer in the Inception network. Then, we model a multivariate Gaussian distribution, which learns the distribution of the feature maps. This multivariate Gaussian distribution has a mean of  and a covariance of , which we use to calculate the FID score. The lower the FID score, the better the model, and the more able it is to generate more diverse images with higher quality. A perfect generative model will have an FID score of zero. The advantage of using the FID score over the Inception score is that it is robust to noise and that it can easily measure the diversity of the images.