Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method that addresses this challenge and efficiently handles meshes with intricate structures. Our method reduces time complexity from O(N) to O(log N) and requires significantly less memory than previous approaches. Building on this innovation, we present a reconstruction algorithm capable of generating complex 2D and 3D shapes from point clouds or multi-view images. Visit our project page (https://sonsang.github.io/dmesh2-project) for source code and supplementary material.