Most well-established and widely used color difference (CD) metrics are handcrafted and subject-calibrated against uniformly colored patches, which do not generalize well to photographic images characterized by natural scene complexities. Constructing CD formulae for photographic images is still an active research topic in imaging/illumination, vision science, and color science communities. In this paper, we aim to learn a deep CD metric for photographic images with four desirable properties. First, it well aligns with the observations in vision science that color and form are linked inextricably in visual cortical processing. Second, it is a proper metric in the mathematical sense. Third, it computes accurate CDs between photographic images, differing mainly in color appearances. Fourth, it is robust to mild geometric distortions (e.g., translation or due to parallax), which are often present in photographic images of the same scene captured by different digital cameras. We show that all these properties can be satisfied at once by learning a multi-scale autoregressive normalizing flow for feature transform, followed by the Euclidean distance which is linearly proportional to the human perceptual CD. Quantitative and qualitative experiments on the large-scale SPCD dataset demonstrate the promise of the learned CD metric.