EvoReg: Versatile and Robust Point Cloud Registration via Multi-Stage Alignment

Point cloud registration methods remain specialized along two axes: most target rigid or non-rigid alignment under either supervised or self-supervised training. To address this fragmentation, we propose EvoReg, a unified multi-stage coarse-to-fine framework that covers all four (rigid/non-rigid) $\times$ (supervised/self-supervised) settings via a single architecture through staged decoupling. Gradient-free CMA-ES pre-alignment over $\mathrm{SE}(3)$ escapes local minima and provides a pose-agnostic initialization, iterative Sinkhorn soft correspondences with confidence-weighted Kabsch refinement tighten the rigid pose, a residual MLP head corrects remaining rigid error, and a conditional VAE predicts a residual non-rigid deformation field on the rigidly-aligned source; each stage inherits and solves a progressively tighter initialization. At inference, four optional training-free modules — concentrated gradient-free $\mathrm{SE}(3)$ search, point-space diffusion denoising, and global and per-point Sinkhorn test-time optimization — combine selectively to trade compute for accuracy without retraining. Trained exclusively on ModelNet40 and evaluated under controlled and real-world protocols spanning ModelNet40, ShapeNet-13, 3DMatch, and FAUST, EvoReg achieves competitive correspondence accuracy and the best distributional alignment among tested baselines — significantly leading them on every Chamfer Distance and Earth Mover's Distance evaluation cell and realizing perfect or near-perfect Chamfer Distance Recall — across all four aforementioned settings. These results show that staged decoupling is an effective architectural principle for unifying rigid and non-rigid point-cloud registration under both pose-supervised and geometric self-supervised training, and position EvoReg as a dynamic and robust method for controlled and real-world registration. The code for this project can be found at: https://anonymous.4open.science/r/EvoReg-0507.