We experimentally and theoretically demonstrate a spatial diametric drive acceleration of two mutually incoherent optical beams in 1D optical lattices under a self-defocusing nonlinearity. The two beams, exciting the modes at the top/bottom edges of the first Bloch band and hence experiencing normal/anomalous diffraction, can bind together and bend in the same direction during nonlinear propagation, analogous to the interplay between two objects with opposite signs of mass that breaks Newton's third law. Their spatial spectrum changes associated with the acceleration are analyzed for different lattice modulations. We find that the acceleration limit is determined by the beam exciting the top band edge that reaches a saturated momentum change prior to the other pairing beam.