SD4R: Decoupling Motion and Correspondence for 4D Gaussian Scene Reconstruction and Editing from Unposed Videos

Unposed dynamic reconstruction from casually captured videos is fundamentally underconstrained, as camera motion, non-rigid dynamics, and temporal correspondence must be inferred jointly from image observations. Beyond the well-known ambiguity between camera and scene motion, we identify correspondence instability as another source of optimization failure: a representation may explain each frame well while gradually losing the identity of the physical elements it is intended to track. % We present , a unified framework that treats unposed dynamic reconstruction as the joint estimation of geometry, motion, and persistent correspondence. The central idea is to decouple motion representation from identity preservation, allowing scene dynamics to remain flexible while correspondence provides a stable temporal reference. We further introduce a compact sparse motion representation that captures coherent non-rigid dynamics through shared continuous structure. % Importantly, the resulting persistent representation naturally extends beyond reconstruction. By linking image-space semantics to temporally persistent scene primitives, enables controllable object-level 4D editing within the same representation. Experiments demonstrate that this formulation improves dynamic reconstruction consistency while supporting localized scene editing.