The reviewers agree that this is a good paper that deserves acceptance. The contributions are useful from a statistical point of view. They also agree that the computational limitations should be put more upfront: the idea of Gaussian smoothing has a limited interest for the neurips community unless one has an efficient algorithm to solve optimal transport between the smoothed densities, which is not the case yet (any method based purely on discretizations, as proposed here, inevitably suffers from the curse of dimensionality). The authors mention in the rebuttal that an idea is to parameterize the dual variable with a neural network, but this leads to an object that is very different from SWD since neural networks have inductive biases. For these reasons, I recommend accept (poster).