This submission received diverging scores and after rebuttal and discussion phase the review scores are 9,6,6. All reviewers recommend acceptance of the paper. There is consensus between the reviewers that this paper represents a contribution to NeurIPS. The submission presents an extension of the recent distortion-perception (DP) trade-off, including classification (CDP). This function presents a contribution to the task of image restoration and can be used for different tasks. The main contribution is the extension from DP to CDP, the proof is well presented and a toy example presents insights and understanding. The main points for improvements as pointed out by the reviewers are experiments over MNIST and denoising. Both points are answered in the rebuttal, please include those in a final revision. - Promised experiments for CIFAR-10. - Additional results beyond image denoising. The rebuttal presents initial results for super-resolution in line with claimed statements in the paper. All reviewers recommend acceptance and with the promised additions from the rebuttal this is a good contribution that is of interest to NeurIPS and beyond. Please make sure to include all other reviewer comments as well in the final version.