We thank all reviewers for their thorough assessment of our paper

We thank all reviewers for their thorough assessment of our paper . This ensures the resulting test produces "well-behaved" We will discuss this further in the revised manuscript, thank you for raising this point. However, insights can also be derived by considering the bound in Theorem 1. Theorem 1 shows that In practice, good performance may also be achieved using other flexible generative models. On the quality of generated samples and stability of p-values - Please kindly refer to the response to Reviewer #3.