Reliable non-rigid point cloud correspondences are important for deformable anatomical registration, embodied perception and manipulation, and dynamic 3D reconstruction. Coarse-to-fine methods reduce computational cost by selecting the top-K coarse regions. However, this pruning may remove weak but correct hypotheses and restrict fine matching to an incomplete search space. We present \paper, a two-stage generative solver that maintains the complete soft matching matrix at both coarse and high resolutions. StageI uses denoising diffusion to estimate a global matching matrix in the compact coarse-resolution space. We then lift this matrix to high resolution while preserving its hierarchy. The lifted matrix is rank-bounded and block-constant. StageII refines it through a conditional transport bridge. We implement the bridge with two types of dynamics: a deterministic endpoint-parameterized conditional Flow Matching (CFM) ODE and a stochastic Brownian-bridge SDE inspired by Schr"odinger bridges. Both variants share the lifted source, a time-conditioned transformer, and a matching-matrix endpoint predictor. Experiments on 4DMatch and 4DLoMatch show that both variants produce more accurate correspondences than the compared methods and improve downstream registration, with larger gains in low-overlap cases. They also improve cross-dataset generalization on CAPE and DeepDeform without target-domain adaptation while using the same deformation solver.
Establishing accurate point-to-point correspondences between non-rigid 3D shapes remains a critical challenge, particularly under non-isometric deformations and topological noise. Existing functional map pipelines suffer from ambiguities that geometric descriptors alone cannot resolve, and spatial inconsistencies inherent in the projection of truncated spectral bases to dense pointwise correspondences. In this paper, we introduce SGMatch, a learning-based framework that couples 3D-lifted semantic cues with trajectory-level feature transport regularization. Specifically, we design a Semantic-Guided Local Cross-Attention module that integrates semantic features from vision foundation models into geometric descriptors while preserving local structural continuity. Furthermore, we adapt conditional flow matching as a time-conditioned feature transport regularizer that promotes spatially coherent point-wise recovery. Experimental results on multiple benchmarks demonstrate that SGMatch achieves competitive performance across near-isometric settings and consistent improvements under non-isometric deformations and topological noise.
Learning reliable correspondences between images and point clouds is fundamental for 2D-3D matching. Despite recent progress in detection-free methods, existing approaches primarily optimize matching within a single model and often struggle to maintain reliable correspondences under challenging conditions such as noisy inputs, low overlap, and ambiguous structures. In this work, we propose TeaMatch, a novel framework that introduces teachability as a criterion for cross-modal representation learning. We define teachability as the ability of a representation to be effectively recovered by weak learners under degraded inputs, reflecting its structural consistency and robustness. To this end, we construct a set of task-specific weak students that simulate common failure modes and train them to imitate the teacher on a training split while evaluating their recoverability on a disjoint meta split. The teacher is then optimized to improve the students' ability to recover reliable correspondences, guided by correspondence-level and geometry-aware constraints. Our framework can be seamlessly integrated into existing coarse-to-fine matching pipelines without additional inference cost. Extensive experiments demonstrate that TeaMatch improves matching robustness and achieves state-of-the-art performance on challenging 2D-3D matching benchmarks.
Visual correspondence across image-to-image (2D-2D), image-to-point cloud (2D-3D), and point cloud-to-point cloud (3D-3D) geometric matching forms the foundation for numerous 3D vision tasks. Despite sharing a similar problem structure, current methods use task-specific designs with separate models for each modality combination. We present UniCorrn, the first correspondence model with shared weights that unifies geometric matching across all three tasks. Our key insight is that Transformer attention naturally captures cross-modal feature similarity. We propose a dual-stream decoder that maintains separate appearance and positional feature streams. This design enables end-to-end learning through stack-able layers while supporting flexible query-based correspondence estimation across heterogeneous modalities. Our architecture employs modality-specific backbones followed by shared encoder and decoder components, trained jointly on diverse data combining pseudo point clouds from depth maps with real 3D correspondence annotations. UniCorrn achieves competitive performance on 2D-2D matching and surpasses prior state-of-the-art by 8% on 7Scenes (2D-3D) and 10% on 3DLoMatch (3D-3D) in registration recall. Project website: https://neu-vi.github.io/UniCorrn