I was curious how they avoid trivial idempotent functions like <i>f</i>(<i>x</i>) = <i>x</i> and it turns out that when they apply the network twice to an image of random noise to check for idempotence, the first instance of the network is rewarded for producing something that isn't changed much by the second instance (encouraging idempotence) but the second instance is punished for not changing an image that was produced by the first instance instead of being sampled from the ground truth (<i>dis</i>couraging idempotence).<p>This technique has a GAN-like adversarial flavor to it, complete with stability issues due to competing objectives. Still, amazing that it works at all.