Hello,
Indeed the Geomloss package is really efficient to compute entropic variants of Optimal Transport. You can have access to the entropic regularized OT or the Sinkhorn divergence. They also provide typical ground cost but you can compute your own. I would suggest to use the Sinkhorn divergence instead of the entropic regularized OT. The later interpolates between OT and MMD losses while the former does not have the separability axiom (i.e OT_eps(a,a) > 0). You can find more details in : https://arxiv.org/abs/1810.08278 22