  Here, we explore the low-level statistics of images generated by
state-of-the-art deep generative models. First, Variational auto-encoder
(VAE~\cite{kingma2013auto}), Wasserstein generative adversarial network
(WGAN~\cite{arjovsky2017wasserstein}) and deep convolutional generative
adversarial network (DCGAN~\cite{radford2015unsupervised}) are trained on the
ImageNet dataset and a large set of cartoon frames from animations. Then, for
images generated by these models as well as natural scenes and cartoons,
statistics including mean power spectrum, the number of connected components in
a given image area, distribution of random filter responses, and contrast
distribution are computed. Our analyses on training images support current
findings on scale invariance, non-Gaussianity, and Weibull contrast
distribution of natural scenes. We find that although similar results hold over
cartoon images, there is still a significant difference between statistics of
natural scenes and images generated by VAE, DCGAN and WGAN models. In
particular, generated images do not have scale invariant mean power spectrum
magnitude, which indicates existence of extra structures in these images.
Inspecting how well the statistics of deep generated images match the known
statistical properties of natural images, such as scale invariance,
non-Gaussianity, and Weibull contrast distribution, can a) reveal the degree to
which deep learning models capture the essence of the natural scenes, b)
provide a new dimension to evaluate models, and c) allow possible improvement
of image generative models (e.g., via defining new loss functions).
