Image Generation Via Minimizing Frechet Distance in Discriminator Feature Space

Khoa D Doan, Saurav Manchanda, Fengjiao Wang, Sathiya Keerthi, Avradeep Bhowmik, Chandan K. Reddy

Abstract: For a given image generation problem, the intrinsic image manifold is often low-dimensional. We use the intuition that it is much better to train the GAN generator by minimizing the distributional distance between real and generated images in a small dimensional feature space representing such a manifold than on the original pixel space. We use the feature space of the GAN discriminator for such a representation. For distributional distance, we employ one of two choices: the Fr\'{e}chet distance or direct optimal transport (OT); these respectively lead us to two new GAN methods: Fr\'{e}chet-GAN and OT-GAN. The idea of employing Fr\'{e}chet distance comes from the success of Fr\'{e}chet Inception 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 its gradient. The Fr\'{e}chet distance estimation requires a significantly less computation time than OT; this allows Fr\'{e}chet-GAN to use a much larger mini-batch size in training than OT. More importantly, we conduct experiments on a number of benchmark datasets and show that Fr\'{e}chet-GAN (in particular) and OT-GAN have significantly better image generation capabilities than the existing representative primal and dual GAN approaches based on the Wasserstein distance.