  We tackle the challenge of disentangled representation learning in generative
adversarial networks (GANs) from the perspective of regularized optimal
transport (OT). Specifically, a smoothed OT loss gives rise to an implicit
transportation plan between the latent space and the data space. Based on this
theoretical observation, we exploit a structured regularization on the
transportation plan to encourage a prescribed latent subspace to be
informative. This yields the formulation of a novel informative OT-based GAN.
By convex duality, we obtain the equivalent view that this leads to perturbed
ground costs favoring sparsity in the informative latent dimensions.
Practically, we devise a stable training algorithm for the proposed informative
GAN. Our experiments support the hypothesis that such regularizations
effectively yield the discovery of disentangled and interpretable latent
representations. Our work showcases potential power of a regularized OT
framework in the context of generative modeling through its access to the
transport plan. Further challenges are addressed in this line.
