  Noise injection has been proved to be one of the key technique advances in
generating high-fidelity images. Despite its successful usage in GANs, the
mechanism of its validity is still unclear. In this paper, we propose a
geometric framework to theoretically analyze the role of noise injection in
GANs. Based on Riemannian geometry, we successfully model the noise injection
framework as fuzzy equivalence on the geodesic normal coordinates. Guided by
our theories, we find that the existing method is incomplete and a new strategy
for noise injection is devised. Experiments on image generation and GAN
inversion demonstrate the superiority of our method.
