We present a simple yet effective technique to boost the performance of 3D point cloud registration. Conventional methods input a distance matrix to a differentiable matching algorithm deterministically, ignoring any uncertainty in upstream distance calculation. Consequently, current methods consider the optimalities of the feature extractor and the matching algorithm independently, leading to sub-optimal performance. We connect them via a non-deterministic information path. To make the algorithm uncertainty-aware, we employ a learning-based matching network module. This modification unifies the estimation process as a single optimization problem, where feature extractors and the matching network are jointly trained, reaching a joint-optimal solution. Experimental results show that our strategy significantly improves the performance of various conventional methods under multiple conditions, including rigid/non-rigid and whole/partial point cloud registration datasets.