The infrared behavior of perturbative quantum gravity is studied using the method developed for QED by Faddeev and Kulish. The operator describing the asymptotic dynamics is derived and used to construct an IR-finite S matrix and space of asymptotic
states. All-orders cancellation of IR divergences is shown explicitly at the level of matrix elements for the example case of gravitational potential scattering. As a practical application of the formalism, the soft part of a scalar scattering amplitude is related to the gravitational Wilson line and computed to all orders.
