We show how a neural network can be trained on individual intrusive listening test scores to predict a distribution of scores for each pair of reference and coded input stereo or binaural signals. We nickname this method the Generative Machine Listener (GML), as it is capable of generating an arbitrary amount of simulated listening test data. Compared to a baseline system using regression over mean scores, we observe lower outlier ratios (OR) for the mean score predictions, and obtain easy access to the prediction of confidence intervals (CI). The introduction of data augmentation techniques from the image domain results in a significant increase in CI prediction accuracy as well as Pearson and Spearman rank correlation of mean scores.