questions raised by each reviewer separately

We thank the reviewers for their close reading, detailed comments, and overall positive assessment. We will improve the flow and formatting of the paper, and fix the references in the final version. As we can see, ADE consistently achieves comparable or the best performance. We are exploring alternative sampling algorithm embeddings, e.g., ADE limitations and how to overcome. See Appendix C for details. ADE, then the parameter tuning requirements for ADE and GANs are comparable, i.e., we tune the inner optimization Re: "[the authors] further conduct T vanilla HMC steps to approximately solve it."