Public data has been frequently used to improve the privacy-accuracy trade-off of differentially private machine learning, but prior work largely assumes that this data come from the same distribution as the private. In this work, we look at how to use generic large-scale public data to improve the quality of differentially private image generation in Generative Adversarial Networks (GANs), and provide an improved method that uses public data effectively. Our method works under the assumption that the support of the public data distribution contains the support of the private; an example of this is when the public data come from a general-purpose internet-scale image source, while the private data consist of images of a specific type. Detailed evaluations show that our method achieves SOTA in terms of FID score and other metrics compared with existing methods that use public data, and can generate high-quality, photo-realistic images in a differentially private manner.