TRoPE: Topology-aware Relative Positional Encoding for 4D Generation

Video-to-4D mesh generation has made substantial progress in recovering dynamic 3D geometry and motion from monocular videos. However, commonly used feed-forward approaches remain prone to sticking artifacts, where geodesically distant vertices move together incorrectly when they become spatially close. We attribute this failure to cross-part motion leakage: spatially nearby yet structurally distant vertices may retrieve similar motion information when motion decoding fails to distinguish spatial proximity from mesh connectivity. To address this issue, we introduce TRoPE, a topology-aware relative positional encoding that incorporates mesh structure into motion generation. TRoPE derives spectral features from the graph Laplacian and constructs pairwise topological relations from distances between multi-scale diffusion features, yielding a stable topology representation across meshes. We further introduce a vertex-wise tail-risk objective that emphasizes persistently high-error vertices to explicitly suppress sticking artifacts. To better characterize and quantify these failures, we introduce MeshSticking-4D, a dedicated benchmark for this failure mode. Experiments on Motion-80 and MeshSticking-4D show that TRoPE consistently suppresses sticking artifacts while maintaining comparable overall generation quality. Compared with the baseline, it reduces the worst-vertex error by 39.4% and lowers the separation failure rate from 49.35% to 34.90%. Additional evaluations across different experiments further demonstrate the general applicability of TRoPE. The code and benchmark will be made publicly available.