  We show that the Schr\"{o}dinger-Newton equation, which describes the
nonlinear time evolution of self-gravitating quantum matter, can be made
compatible with the no-signaling requirement by elevating it to a stochastic
differential equation. In the deterministic form of the equation, as studied so
far, the nonlinearity would lead to diverging energy corrections for localized
wave packets and would create observable correlations admitting
faster-than-light communication. By regularizing the divergencies and adding
specific random jumps or a specific Brownian noise process, the effect of the
nonlinearity vanishes in the stochastic average and gives rise to a linear and
Galilean invariant evolution of the density operator.
