Title: SpectralFlow: Geometry-Aware Mesh Animation via Spectral Coefficient Diffusion
Primary area: learning on graphs and other geometries & topologies
Keywords: 4D generation, geometry, mesh

Abstract: Generating realistic 3D shape sequences (or 4D shapes) conditioned on actions is challenging due to high-dimensional, non-linear, and temporally coherent deformations across diverse shapes. In this work, we introduce SpectralFlow, a diffusion-based framework for action-conditioned 4D shape generation in the Laplacian spectral domain. Instead of modeling raw vertex trajectories or mesh offsets, we represent each shape using a fixed set of Laplacian eigenbases and a sequence of time-varying spectral coefficients, capturing intrinsic geometry and temporal dynamics compactly. By aligning eigenbases across shapes via sign correction and basis transformation, we establish a shared, topology-agnostic spectral space that supports consistent learning across identities and motion types. A conditional diffusion model is trained to generate spectral trajectories based on the input shape and target action, producing smooth, coherent, and semantically aligned mesh sequences. Our method avoids purely implicit modeling, which typically requires large-scale data, by leveraging lightweight geometric representations for controllable 4D shape generation. Extensive experiments show that SpectralFlow outperforms prior methods in reconstruction quality and motion generalization. Our project page is \url{https://specflow3d.github.io.}