We prove that the distribution of eigenvectors of generalizedWigner matrices
is universal both in the bulk and at the edge. This includes a probabilistic version of local
quantum unique ergodicity and asymptotic normality of the eigenvector entries. The
proof relies on analyzing the eigenvector flow under the Dyson Brownian motion. The
key new ideas are: (1) the introduction of the eigenvector moment flow, a multi-particle
random walk in a random environment, (2) an effective estimate on the regularity of this
flow based on maximum principle and (3) optimal finite speed of propagation holds for
the eigenvector moment flow with very high probability.