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.
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