DMM-Align: Closed-Loop Optimization for 2D-3D Registration with Dual-Role Diffusion

2D-3D registration remains brittle in challenging scenarios such as low overlap, occlusion, repetitive structures, and severe cross-modal ambiguity. A key reason is that existing methods improve representation learning, correspondence estimation, or pose computation in isolation, while the dominant failure mode is inherently cross-level, where errors propagate between features, correspondences, and pose. To address this limitation, we propose DMM-Align: Diffusion-based Matching Matrix Alignment, a closed-loop framework that couples correspondence refinement, pose estimation, and representation learning through a shared differentiable geometric state. Our method leverages diffusion in two coordinated roles: a geometry-aware diffusion process refines the soft matching matrix for robust correspondence estimation, while a geometry-conditioned diffusion teacher injects pose-induced supervision back into feature learning. These processes are connected via a differentiable geometric hinge that converts correspondences into a global pose and exposes geometric inconsistency to upstream modules. Extensive experiments on 7-Scenes and RGB-D Scenes V2 demonstrate that DMM-Align consistently outperforms strong baselines, especially under low-overlap and heavy-occlusion conditions, highlighting the effectiveness of closed-loop geometric feedback for robust 2D-3D registration.