Intriguing Properties of Modern GANs

Modern GANs achieve remarkable performance in terms of generating realistic and diverse samples. This has led many to believe that ``GANs capture the training data manifold''. In this work we show that this interpretation is wrong. We empirically show that the manifold learned by modern GANs does not fit the training distribution: specifically the manifold does not pass through the training examples and passes closer to out-of-distribution images than to in-distribution images. We also investigate the distribution over images implied by the prior over the latent codes and study whether modern GANs learn a density that approximates the training distribution. Surprisingly, we find that the learned density is very far from the data distribution and that GANs tend to assign higher density to out-of-distribution images. Finally, we demonstrate that the set of images used to train modern GANs are often not part of the typical set described by the GANs' distribution.

Posterior Sampling for Image Restoration using Explicit Patch Priors

Almost all existing methods for image restoration are based on optimizing the mean squared error (MSE), even though it is known that the best estimate in terms of MSE may yield a highly atypical image due to the fact that there are many plausible restorations for a given noisy image. In this paper, we show how to combine explicit priors on patches of natural images in order to sample from the posterior probability of a full image given a degraded image. We prove that our algorithm generates correct samples from the distribution $p(x|y) \propto \exp(-E(x|y))$ where $E(x|y)$ is the cost function minimized in previous patch-based approaches that compute a single restoration. Unlike previous approaches that computed a single restoration using MAP or MMSE, our method makes explicit the uncertainty in the restored images and guarantees that all patches in the restored images will be typical given the patch prior. Unlike previous approaches that used implicit priors on fixed-size images, our approach can be used with images of any size. Our experimental results show that posterior sampling using patch priors yields images of high perceptual quality and high PSNR on a range of challenging image restoration problems.