  Image steganography is the process of concealing secret information in images
through imperceptible changes. Recent work has formulated this task as a
classic constrained optimization problem. In this paper, we argue that image
steganography is inherently performed on the (elusive) manifold of natural
images, and propose an iterative neural network trained to perform the
optimization steps. In contrast to classical optimization methods like L-BFGS
or projected gradient descent, we train the neural network to also stay close
to the manifold of natural images throughout the optimization. We show that our
learned neural optimization is faster and more reliable than classical
optimization approaches. In comparison to previous state-of-the-art
encoder-decoder-based steganography methods, it reduces the recovery error rate
by multiple orders of magnitude and achieves zero error up to 3 bits per pixel
(bpp) without the need for error-correcting codes.
