Looks like a complex topic, but the code is small enough to help remove the rust from my math gears. I guess everybody would want it ported to CUDA/OpenCL/Vulkan?

it is weird that everyone uses this relatively old EMD solver.

in this case the WGAN doesn’t actually compute the discrete EMD like that. instead it uses some constraints in the optimization process (gradient clipping), which it can be argued make the training objective equivalent in the limit to minimizing continuous Wasserstein distance (between probability distributions).

FWIW, the code on that page computes EMD for histograms, which is basically the easy case. The EMD over a high dimensional continuous distribution like images is intractable by comparison.