  Propagating intrinsic localised modes (discrete breathers) exist in the
dissipative driven sine-Gordon chain as attractors of the dynamics. Thermal
fluctuations induce random transitions between attracting configurations
corresponding to opposite signs of the propagation velocity, effecting a
diffusive motion of the breather. Results for the mean value and the variance
of the position from numerical simulations (Heun method) are compared with
predictions from a two-parameter model developed in this paper.
