There is growing concern about image privacy due to the popularity of social media and photo devices, along with increasing use of face recognition systems. However, established image de-identification techniques are either too subject to re-identification, produce photos that are insufficiently realistic, or both. To tackle this, we present a novel approach for image obfuscation by manipulating latent spaces of an unconditionally trained generative model that is able to synthesize photo-realistic facial images of high resolution. This manipulation is done in a way that satisfies the formal privacy standard of local differential privacy. To our knowledge, this is the first approach to image privacy that satisfies $\varepsilon$-differential privacy \emph{for the person.}