Though generative adversarial networks (GANs) areprominent models to generate realistic and crisp images,they often encounter the mode collapse problems and arehard to train, which comes from approximating the intrinsicdiscontinuous distribution transform map with continuousDNNs. The recently proposed AE-OT model addresses thisproblem by explicitly computing the discontinuous distribu-tion transform map through solving a semi-discrete optimaltransport (OT) map in the latent space of the autoencoder.However the generated images are blurry. In this paper, wepropose the AE-OT-GAN model to utilize the advantages ofthe both models: generate high quality images and at thesame time overcome the mode collapse/mixture problems.Specifically, we first faithfully embed the low dimensionalimage manifold into the latent space by training an autoen-coder (AE). Then we compute the optimal transport (OT)map that pushes forward the uniform distribution to the la-tent distribution supported on the latent manifold. Finally,our GAN model is trained to generate high quality imagesfrom the latent distribution, the distribution transform mapfrom which to the empirical data distribution will be con-tinuous. The paired data between the latent code and thereal images gives us further constriction about the generator.Experiments on simple MNIST dataset and complex datasetslike Cifar-10 and CelebA show the efficacy and efficiency ofour proposed method.
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