Adaptive normalized cross-correlation (ANCC) cost function works well between images under photometric distortions, but its heavy computational burden often limits its applications. To overcome this limitation, this paper proposes a robust and efficient computational framework, called ANCC flow, designed for establishing dense correspondences between images under severe photometric variations. We first simplify the weight of ANCC in an asymmetric manner by considering a source image weight only. It is then efficiently computed by applying constant-time edge-aware filters without loss of its matching accuracy. Additionally, to deal with a large discrete label space effectively, which is a challenging issue in a flow field estimation, we propose a randomized label space sampling strategy similar to PatchMatch filer (PMF) optimization. The robustness of the asymmetric ANCC and the cost filter is further enhanced through an evolving weight computation, where a flow field computed in a previous iteration is utilized to build current edge-aware weights. Experimental results demonstrate the outstanding performance of ANCC flow in many cases of dense correspondence estimations under severe photometric and geometric variations.