Reviews: Multi-marginal Wasserstein GAN

Multi Marginal Wasserstein GAN's goal is to match a source domain distribution to multiple target domain distributions. While dedicated GAN frameworks exist, as noted by the authors (CycleGAN, StarGAN, …), their generated samples suffer from blurriness, especially when resulting from multiple targets. Moreover, the main statement of this work is that MWGAN is theoretically motivated, unlike previous works. Computing the multi marginal Wasserstein distance between several domains is intractable in its primal form. Thus, as proposed in WGAN, the authors express their problem in the dual form, resulting in equation 1. Since, the dual formulation is a maximization problem under infinite constraint, which remains intractable, the authors simplify the problem by only considering it on its empirical version (equation 2).