  Training even moderately-sized generative models with differentially-private
stochastic gradient descent (DP-SGD) is difficult: the required level of noise
for reasonable levels of privacy is simply too large. We advocate instead
building off a good, relevant representation on an informative public dataset,
then learning to model the private data with that representation. In
particular, we minimize the maximum mean discrepancy (MMD) between private
target data and a generator's distribution, using a kernel based on perceptual
features learned from a public dataset. With the MMD, we can simply privatize
the data-dependent term once and for all, rather than introducing noise at each
step of optimization as in DP-SGD. Our algorithm allows us to generate
CIFAR10-level images with $\epsilon \approx 2$ which capture distinctive
features in the distribution, far surpassing the current state of the art,
which mostly focuses on datasets such as MNIST and FashionMNIST at a large
$\epsilon \approx 10$. Our work introduces simple yet powerful foundations for
reducing the gap between private and non-private deep generative models. Our
code is available at \url{https://github.com/ParkLabML/DP-MEPF}.
