This paper presents an interesting perspective to the domain generalization problem, proposing to learn representations that are condtional-invariant across the source datsets. Analysis and theory on simple datasets are used to motivate the problem and approach, and results are shown on larger datasets. Some reviewer concerns were expressed in terms of the methodology and claims, but the rebuttal largely addressed these. Overall, the paper presents a well-reasoned approach that is theoretically-motivated. The authors should make sure to especially calibrate their empirical claims based on the reviewer feedback.