  In the past few years, Generative Adversarial Networks (GANs) have
dramatically advanced our ability to represent and parameterize
high-dimensional, non-linear image manifolds. As a result, they have been
widely adopted across a variety of applications, ranging from challenging
inverse problems like image completion, to problems such as anomaly detection
and adversarial defense. A recurring theme in many of these applications is the
notion of projecting an image observation onto the manifold that is inferred by
the generator. In this context, Projected Gradient Descent (PGD) has been the
most popular approach, which essentially optimizes for a latent vector that
minimizes the discrepancy between a generated image and the given observation.
However, PGD is a brittle optimization technique that fails to identify the
right projection (or latent vector) when the observation is corrupted, or
perturbed even by a small amount. Such corruptions are common in the real
world, for example images in the wild come with unknown crops, rotations,
missing pixels, or other kinds of non-linear distributional shifts which break
current encoding methods, rendering downstream applications unusable. To
address this, we propose corruption mimicking -- a new robust projection
technique, that utilizes a surrogate network to approximate the unknown
corruption directly at test time, without the need for additional supervision
or data augmentation. The proposed method is significantly more robust than PGD
and other competing methods under a wide variety of corruptions, thereby
enabling a more effective use of GANs in real-world applications. More
importantly, we show that our approach produces state-of-the-art performance in
several GAN-based applications -- anomaly detection, domain adaptation, and
adversarial defense, that benefit from an accurate projection.
