  The privacy implications of generative adversarial networks (GANs) are a
topic of great interest, leading to several recent algorithms for training GANs
with privacy guarantees. By drawing connections to the generalization
properties of GANs, we prove that under some assumptions, GAN-generated samples
inherently satisfy some (weak) privacy guarantees. First, we show that if a GAN
is trained on m samples and used to generate n samples, the generated samples
are (epsilon, delta)-differentially-private for (epsilon, delta) pairs where
delta scales as O(n/m). We show that under some special conditions, this upper
bound is tight. Next, we study the robustness of GAN-generated samples to
membership inference attacks. We model membership inference as a hypothesis
test in which the adversary must determine whether a given sample was drawn
from the training dataset or from the underlying data distribution. We show
that this adversary can achieve an area under the ROC curve that scales no
better than O(m^{-1/4}).
