SpectralWeave: A shared spectral framework for Native 4D Mesh Generation

Native 4D mesh generation animates an unrigged input mesh from a semantic action condition while preserving its vertex indexing and connectivity. Sharing motion across independently meshed inputs requires common learning coordinates that retain reconstruction on each input topology. We introduce **SpectralWeave**, a framework for native 4D mesh generation that builds its spectral motion representation from the geometric structure inherent in the input mesh. A native Laplacian basis computed from each mesh remains fixed throughout the sequence, representing motion through compact coefficient trajectories that decode directly on the input vertices without a learned mesh decoder. However, native coefficients remain difficult to compare across identities because their bases differ. We align native spectral coordinates through jointly estimated adapters, establishing shared coordinates while preserving each mesh's native reconstruction subspace. We then use partial surface correspondences for alignment and condition motion diffusion on the action and input morphology. We decode the generated shared coefficients and refine the sequence to preserve local details. Experiments in separate animal and human domains demonstrate better motion accuracy and surface quality on new identities than the compared methods. Ablations support shared spectral coordinates, morphology conditioning, and geometric refinement. See the Project page for more demos: [Project page](https://anoymouscell.github.io/spectralweave).