The pervasiveness of camera technology in every-day life begets a modern reality in which images of individuals are routinely captured on a daily basis. Although this has enabled many benefits, it also infringes on personal privacy. To mitigate the loss of privacy, researchers have investigated methods of facial obfuscation in images. A promising direction has been the work in the k-same family of methods which employ the concept of k-anonymity from database privacy. However, there are a number of deficiencies of k-anonymity which carry over to the k-same methods, detracting from their usefulness in practice. In this paper, we first outline several of these deficiencies and discuss their implications in the context of facial obfuscation. We then develop the first framework to apply the formal privacy guarantee of differential privacy to facial obfuscation in generative machine learning models for images. Next, we discuss the theoretical improvements in the privacy guarantee which make this approach more appropriate for practical usage. Our approach provides a provable privacy guarantee which is not susceptible to the outlined deficiencies of k-same obfuscation and produces photo-realistic obfuscated output. Finally, while our approach provides a stronger privacy guarantee, we demonstrate through experimental comparisons that it can achieve comparable utility to k-same approaches in the context of preservation of demographic information in the images. The preservation of such information is of particular importance for enabling effective data mining on the obfuscated images.