Analysis of the statistical properties of natural images has played a vital role in the design of no-reference (NR) image quality assessment (IQA) techniques. In this paper, we propose parametric models describing the general characteristics of chromatic data in natural images. They provide informative cues for quantifying visual discomfort caused by the presence of chromatic image distortions. The established models capture the correlation of chromatic data between spatially adjacent pixels by means of color invariance descriptors. The use of color invariance descriptors is inspired by their relevance to visual perception, since they provide less sensitive descriptions of image scenes against viewing geometry and illumination variations than luminances. In order to approximate the visual quality perception of chromatic distortions, we devise four parametric models derived from invariance descriptors representing independent aspects of color perception: 1) hue; 2) saturation; 3) opponent angle; and 4) spherical angle. The practical utility of the proposed models is examined by deploying them in our new general-purpose NR IQA metric. The metric initially estimates the parameters of the proposed chromatic models from an input image to constitute a collection of quality-aware features (QAF). Thereafter, a machine learning technique is applied to predict visual quality given a set of extracted QAFs. Experimentation performed on large-scale image databases demonstrates that the proposed metric correlates well with the provided subjective ratings of image quality over commonly encountered achromatic and chromatic distortions, indicating that it can be deployed on a wide variety of color image processing problems as a generalized IQA solution.