This manuscript proposes novel approaches for efficiently computing expectations with respect to generative models under certain assumptions. The reviewers discuss the clarity and novelty of the main results as a strength of the manuscript. On the other hand, the reviewers point out weaknesses related to the strength of the assumptions and the extent to which they may hold on real data, and may have wide applicability. Reviewers are concerned about sufficient empirical evaluation, perhaps exploring some real-world settings where the proposed approach may be relevant. There are also issues with the conciseness of the writing in some parts. The authors are encouraged to carefully incorporate the feedback from reviewers in subsequent versions.