Since the work Sidoravicius-Sznitman’04, Berger-Biskup’07, and Mathieu-Piatnitski’07, it is well-known that the random walk on the infinite cluster of supercritical Bernoulli percolation will converge to the Brownian motion. This talk aims to prove that, the diffusivity is infinitely differentiable in this regime, which confirms a conjecture by Kozlov [Uspekhi Mat. Nauk 44 (1989), no. 2(266), pp 79–120]. The proof relies on the homogenization theory, the perturbation argument, and the renormalization of geometry. Several new combinatorial techniques including the cluster-growth decomposition, and the hole separation, are developed. This talk is based on a joint work with Wenhao Zhao (EPFL).