We introduce a distortion measure for images, Wasserstein distortion, that simultaneously generalizes pixel-level fidelity on the one hand and realism or perceptual quality on the other through a width parameter σ. Wasserstein distortion arises from an information theoretical effort of unifying fidelity distortion and realism distortion into one framework, with ideas coming from models of the early human visual system, in the form of an optimizable metric in the mathematical sense. We first show theoretical results for Wasserstein distortion, including continuity results for Wasserstein distortion in the extreme cases of pure fidelity and pure realism, metric properties, and coding theorems for compression under Wasserstein distortion focusing on the regime in which both the rate and the distortion are small. We then show a scheme for automatically choosing the σ parameter for any given image. Lastly, we present experimental results, including texture and image reproduction, and human opinion prediction, to illustrate its utility.