the MCMC perspective, we could treat these (already learned) models as proposals for the approximate MH-algorithm

We thank all of the reviewers for their valuable feedback and detailed comments. That is "improvement and justification of any implicit sampler". We know that in practice, even state-of-the-art generative models yield "unrealistic" samples, hence, are biased. (Algorithm 3). Based on our theoretical analysis, we derive different losses for the discriminator (Table 1 in the paper).