since pot.emd2 returns accurate distance, how could the results have gradient when torch tensor passed in?

i thought only sinkhorn methods enables gradient calculation due to iterative evaluation. how could EMD also support gradient calculation?

It actually returns sub-gradients because indeed it is not differentiable but similarly to relu that is not differentiable, sub-gradient are quite sufficient for many optimization tasks (but less stable especially if you compute gradients wrt weights)