  Generative convolutional deep neural networks, e.g. popular GAN
architectures, are relying on convolution based up-sampling methods to produce
non-scalar outputs like images or video sequences. In this paper, we show that
common up-sampling methods, i.e. known as up-convolution or transposed
convolution, are causing the inability of such models to reproduce spectral
distributions of natural training data correctly. This effect is independent of
the underlying architecture and we show that it can be used to easily detect
generated data like deepfakes with up to 100% accuracy on public benchmarks.
  To overcome this drawback of current generative models, we propose to add a
novel spectral regularization term to the training optimization objective. We
show that this approach not only allows to train spectral consistent GANs that
are avoiding high frequency errors. Also, we show that a correct approximation
of the frequency spectrum has positive effects on the training stability and
output quality of generative networks.
