  We present a novel, end-to-end approach to align CAD models to an 3D scan of
a scene, enabling transformation of a noisy, incomplete 3D scan to a compact,
CAD reconstruction with clean, complete object geometry. Our main contribution
lies in formulating a differentiable Procrustes alignment that is paired with a
symmetry-aware dense object correspondence prediction. To simultaneously align
CAD models to all the objects of a scanned scene, our approach detects object
locations, then predicts symmetry-aware dense object correspondences between
scan and CAD geometry in a unified object space, as well as a nearest neighbor
CAD model, both of which are then used to inform a differentiable Procrustes
alignment. Our approach operates in a fully-convolutional fashion, enabling
alignment of CAD models to the objects of a scan in a single forward pass. This
enables our method to outperform state-of-the-art approaches by $19.04\%$ for
CAD model alignment to scans, with $\approx 250\times$ faster runtime than
previous data-driven approaches.
