Abstract: Recent probabilistic methods for 3D triangular meshes have shown promise in capturing diverse shapes by managing mesh connectivity in a differentiable manner. However, these methods are often limited by high computational costs that scale disproportionately with the level of detail, restricting their applicability for complex shapes requiring high face density. In this work, we introduce a novel differentiable mesh processing method that addresses these computational challenges in both 2D and 3D. Our method reduces time complexity from $O(N)$ to $O(\log N)$ and requires significantly less memory than previous approaches, enabling us to handle far more intricate structures. Building on this innovation, we present a reconstruction algorithm capable of generating complex 2D and 3D shapes from point clouds or multi-view images. We demonstrate its efficacy on various objects exhibiting diverse topologies and geometric details.