In four-dimensional asymptotically flat spacetimes, the infinite tower of soft graviton modes is known to generate a w(1+infinity) symmetry algebra at tree-level.  In this talk, I will review this symmetry and demonstrate that it acts non-trivially on massive scalar particles.  The symmetry action is derived from previously-discovered soft graviton theorems, which characterize universal behavior of gravitational scattering amplitudes.  I will present a generalization of earlier analyses that were formerly specifically tailored to the scattering of massless particles.  These results clarify that w(1+infinity) is a universal feature of tree-level gravitational scattering in four-dimensional asymptotically flat spacetimes and originates from minimally-coupled gravitational interactions.