GM-R^2: Generative Matching Learning for Unsupervised Geometric Representation and Registration

This paper proposes GM-R 2 , a novel Generative Matching Learning framework for unsupervised geometric descriptor learning and correspondence matching. By reformulating descriptor learning as geometry-conditioned crossview image generation, GM-R 2 leverages the proxy supervisory signal from structurally aligned view synthesis to implicitly enforce feature consistency across correspondence, enabling robust 3D matching. To instantiate GM-R 2 , we introduce Denoising-Agnostic Coupled ControlNet conditioned on range maps as the required geometry-conditioned cross-view generator. It effectively extends vanilla Con-trolNet from single-view to cross-view generation via a coupled range-map input design, and further removes the dependency on noisy latents to enable geometry-only inference, as required in practical 3D matching. Particularly, we present Auto-FoV Equirectangular Projection, an intrinsics-free point cloud-to-range mapping scheme that adaptively zooms into the angular region occupied by the narrow-FoV input, enabling dense and high-fidelity rangemap generation. Extensive experiments on 3DMatch and ScanNet datasets verify the superior unsupervised registration accuracy of our proposed method, even surpassing fully-supervised methods. Overlap: 0.041 Inlier Ratio: 0.557 Overlap: 0.065 Inlier Ratio: 0.492 Overlap: 0.202 Inlier Ratio: 0.701 Overlap: 0.154 Inlier Ratio: 0.498 Overlap: 0.121 Inlier Ratio: 0.545 Overlap: 0.213 Inlier Ratio: 0.660