This document discusses various methods for calculating Wasserstein distance between probability distributions, including: - Sliced Wasserstein distance, which projects distributions onto lower-dimensional spaces to enable efficient 1D optimal transport calculations. - Max-sliced Wasserstein distance, which focuses sampling on the most informative projection directions. - Generalized sliced Wasserstein distance, which uses more flexible projection functions than simple slicing, like the Radon transform. - Augmented sliced Wasserstein distance, which applies a learned transformation to distributions before projecting, allowing more expressive matching between distributions. These sliced/generalized Wasserstein distances have been used as loss functions for generative models with promising