Abstract: This paper describes a new acceleration technique for rendering algorithms like path tracing, that use so called gathering random walks. Usually in path tracing, each traced path is used in order to compute a contribution to only a single point on the virtual screen. We propose to combine paths traced through nearby screen points in such a way that each path contributes to multiple screen points in a provably good way. Our approach is unbiased and is not restricted to diffuse light scattering. It complements previous image noise reduction techniques for Monte Carlo ray tracing. We observe speed-ups in the computation of indirect illumination of one order of magnitude.