Accurate prediction of local distortion visibility thresholds is critical in many image and video processing applications. Existing methods require an accurate modeling of the human visual system, and are derived through pshycophysical experiments with simple, artificial stimuli. These approaches, however, are difficult to generalize to natural images with complex types of distortion. In this paper, we explore a different perspective, and we investigate whether it is possible to learn local distortion visibility from image quality scores. We propose a convolutional neural network based optimization framework to infer local detection thresholds in a distorted image. Our model is trained on multiple quality datasets, and the results are correlated with empirical visibility thresholds collected on complex stimuli in a recent study. Our results are comparable to state-of-the-art mathematical models that were trained on phsycovisual data directly. This suggests that it is possible to predict psychophysical phenomena from visibility information embedded in image quality scores.