  Generative adversarial networks constitute a powerful approach to generative
modeling. While generated samples often are indistinguishable from real data,
mode-collapse may occur and there is no guarantee that they will follow the
true data distribution. For scientific applications in particular, it is
essential that the true distribution is well captured by the generated
distribution. In this work, we propose a method to ensure that the
distributions of certain generated data statistics coincide with the respective
distributions of the real data. In order to achieve this, we add a new loss
term to the generator loss function, which quantifies the difference between
these distributions via suitable f-divergences. Kernel density estimation is
employed to obtain representations of the true distributions, and to estimate
the corresponding generated distributions from minibatch values at each
iteration. When compared to other methods, our approach has the advantage that
the complete shapes of the distributions are taken into account. We evaluate
the method on a synthetic dataset and a real-world dataset and demonstrate
improved performance of our approach.
