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For a given image generation problem, the intrinsic image manifold is oftenlow dimensional. We use the intuition that it is much better to train the GANgenerator by minimizing the distributional distance between real and generatedimages in a small dimensional feature space representing such a manifold thanon the original pixel-space. We use the feature space of the GAN discriminatorfor such a representation. For distributional distance, we employ one of twochoices: the Fr\'{e}chet distance or direct optimal transport (OT); theserespectively lead us to two new GAN methods: Fr\'{e}chet-GAN and OT-GAN. Theidea of employing Fr\'{e}chet distance comes from the success of Fr\'{e}chetInception Distance as a solid evaluation metric in image generation.Fr\'{e}chet-GAN is attractive in several ways. We propose an efficient,numerically stable approach to calculate the Fr\'{e}chet distance and itsgradient. The Fr\'{e}chet distance estimation requires a significantly lesscomputation time than OT; this allows Fr\'{e}chet-GAN to use much largermini-batch size in training than OT. More importantly, we conduct experimentson a number of benchmark datasets and show that Fr\'{e}chet-GAN (in particular)and OT-GAN have significantly better image generation capabilities than theexisting representative primal and dual GAN approaches based on the Wassersteindistance.

Image Generation Via Minimizing Fr\'echet Distance in Discriminator Feature Space