[D] How to compute the distance between two high-dimensional distributions?

Hey all,

I am generating a set of extra MNIST digits for a research project, and I am interested in somehow computing the distance between the distribution these digits represent and the distribution that the MNIST train set, for example, represents. The issue is that it seems like typical methods (Jensen-Shannon, Wasserstein, etc.) collapse at high dimensions. Is there a consensus solid approach to do this nowadays? Thanks!

compute computing digits distribution example extra hey issue machinelearning mnist project research set