In stereo matching, computing matching cost or similarity between pixels across different images is one of the main steps to get reliable results. More accurate and robust matching cost can be obtained by aggregating per-pixel raw matching cost within the predefined support area. Here, it is very important to aggregate only valid supports from neighbouring pixels. However, unfortunately, it is hard to evaluate the validity of the supports from neighbours beforehand. To resolve this problem, we propose a new method for the matching cost computation based on the nonlinear diffusion. The proposed method helps to aggregate truly valid supports from neighbouring pixels and does not require any local stopping criterion of iteration. This is achieved by using disparity-dependent support weights that are also updated at every iteration. As a result, the proposed method combined with a simple winner-take-all disparity selection method yields good results not only in homogeneous areas but also in depth discontinuity areas as the iteration goes on without the critical degradation of performance. In addition, when combined with global methods for the disparity selection, the proposed method truly improve the matching performance.