Aligning a partial, real-world 3D face scan to a canonical representation requires solving two coupled problems at once: estimating the rigid pose that brings the scan into a common frame, and completing the facial shape in regions the scan never observed. Existing pipelines typically decouple these steps, running a generic point-cloud registration front end followed by a separate non-rigid fitting or deformation stage. Building on the GeoTransformer superpoint-matching architecture, we propose a single network that predicts both a rigid pose and a shape-complete point cloud in one forward pass: a cross-attention regressor, conditioned on transformer point features and predicted coarse correspondences, maps a partial scan to per-patch coefficients of a 3D morphable face model learned offline from a corpus of 8,000 identities. The resulting morphed template is then used, in the same forward pass, as the target for fine-grained Sinkhorn matching and rigid pose estimation, supervised purely by geometric alignment to ground-truth morphed geometry, so no hand-labeled coefficients are required. Against six classical and learned non-rigid registration baselines on held-out identities, our method leads the strongest ones by 3-4 times on per-vertex error and baselines that collapse the head onto the visible region by more than an order of magnitude, and is simultaneously the most accurate and fastest method on ground-truth-free scans from two independent real-scan datasets, NoW and NPHM. Code will be made publicly available.

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