Overall, the reviewers were quite satisfied with the paper, which provides a conditional gradient algorithm to solve a Gromov-partial Wasserstein problem and theory and experiments to support the algorithms. However I, the area chair, and the senior area chair have discussed this paper in detail and we have a more mitigated opinion. I particular we found several claims to be misleading and they should be changed for the final version to be accepted : - "but when it comes with exact solutions, almost no partial formulation of neither Wasserstein nor Gromov-Wasserstein are available yet." This is not true (partial OT is a standard linear program) so this claim must be removed; - The authors should not claim (such as in the current conclusion) to have introduced the "dummy" point technique for partial optimal transport, which is classical (R#1 gave an example of reference but this is common practice, see e.g. this other reference Pele, Werman, ICCV 2009 "Fast and Robust Earth Mover’s Distances"). Overall, the contributions from the algorithmic optimal transport point of view are rather minor, and we advise the authors to emphasize more on their application to PU learning instead. Other remarks: - please check the grammar (in particular the abstract has several mistakes) - the paper by Solomon et al 2016 "Entropic Metric Alignment for Correspondence Problems" is very relevant in paragraph 2 of the introduction; - what do you mean by "xi" is bounded? (a fixed scalar is always bounded); - the broader impact section is not meant to discuss technical facts, but rather should be about the potential societal impact of the work, if any (see author's guidelines).