We thank all our reviewers for their detailed and insightful comments; we$believe they will help improve the paper.

Reviewer 1: We will augment the code and report the LL bound for the IWAE
experiment. 

We agree with Reviewer 2 that Jensens inequality for \sqrt could be an
alternative and potentially easier way to introduce some of the results. But we
would loose the interpretation that this definition corresponds to regularizing
with the Bhattacharyya distance and we would loose the methods to perform
sampling and inpainting with p*. We therefore intend to stay with the current
formulation.

Reviewer 3: We will rephrase the efficiency claim to highlight that the LL
estimation is more efficient, not inference in general. We will also emphasize
that p* corresponds to an undirected model and add RBM/DBM results to table 3
for comparison. The results in table 3 are not cherry-picked but the result of
thoroughly experimentation. They also closely match the estimates reported in
the respective original publications.