Need the input to be positive?

[bbsun]

For conventional OT defination, it is the distance between to probablity distribution and the input should be nonegative. But in the code of examples, I find x = np.random.normal(0, 1, (batch_size, dim)) so that x can be negative. Can this be an issue?

[rythei]

I'm not sure I understand exactly what you mean -- the OT/Wasserstein distance does indeed define a metric between probability measures, which are positive (and take value in [0,1]). But random variables distributed according to those measures can surely be positive or negative. In the case you mentioned, if X is N(0,1), then its distribution is (2*pi)^(-1/2)exp(-x^2/2)dx, which is positive, but it defines a distribution over all of R.