Title: From Distance to Dependency: A Paradigm Shift of Full-reference Image Quality Assessment. Abstract: Deep learning-based full-reference image quality assessment (FR-IQA) models typically rely on the feature distance between the reference and distorted images. However, the underlying assumption of these models that the distance in the deep feature domain could quantify the quality degradation does not scientifically align with the invariant texture perception, especially when the images are generated artificially by neural networks.  In this paper, we bring a radical shift in inferring the quality with learned features and propose the Deep Image Dependency (DID) based FR-IQA model.  The feature dependency facilitates the comparisons of deep learning features in a high-order manner with Brownian distance covariance, which is characterized by the joint distribution of the features from reference and test images, as well as their marginal distributions. This enables the quantification of the feature dependency against nonlinear transformation, which is far beyond the computation of the numerical errors in the feature space. Experiments on image quality prediction, texture image similarity, and geometric invariance validate the appealing performance of our proposed measure, and the implementation will be publicly available.