We would like to thank all the reviewers for their thoughtful and generally positive comments. We will include more related work and cite them more precisely. We will add more kernel learning methods such as IKL [4]. Even comparing to these results, ours is still much better. Our proposed method learns the kernel using WGF.

Weaknesses: It seems there are closely related works are not cited and discussed in the paper (see Relation to prior work). As mentioned in section 1 "Once the heat kernel is learned, it can be directly applied to a large family of kernel-based machine learning models", it seems will be better we can see more supports for this argument for example combine the proposed HK algorithm with SVM or other kernel machines, in additional to SVGD and DGM. In particular, apply proposed HK (or HK-DK) to DGMs is a quite details involved process vs. it will be more clear to evaluate the performance of proposed heat-kernel with relative clean kernel methods together. As one key empirical results in section 4.3 for Deep Generative Models, there are some concerns for the proposed HK & HK-DK. Also, under the metric IS data CIFAR-10 RetNet, it seems Auto-GAN [34] achieved better performance than proposed HK and on bar with HK-DK.