# Cepheid

In sparse-to-dense mesh motion completion, residual priors trained on one geometry family often fail to beat parameter-free harmonic extension, because residual amplitude varies by more than an order of magnitude across families and densities while the target motion is unknown at test time. Cepheid learns only a dimensionless residual structure and recovers physical amplitude from observables plus a lightweight correction fitted on training sources. The unified model stays below harmonic extension on all five evaluated families, cutting error by 15.6% on an unseen cloth sheet and 10.1% on procedural legged bodies, without skeletons, registration, or cross-mesh correspondence.

In sparse-to-dense mesh motion completion, residual priors trained on one geometry family often fail to beat parameter-free harmonic extension, because residual amplitude varies by more than an order of magnitude across families and densities while the target motion is unknown at test time. Cepheid learns only a dimensionless residual structure and recovers physical amplitude from observables plus a lightweight correction fitted on training sources. The unified model stays below harmonic extension on all five evaluated families, cutting error by 15.6% on an unseen cloth sheet and 10.1% on procedural legged bodies, without skeletons, registration, or cross-mesh correspondence.