Figure 2: Overview of PAIR3D. PAIR3D aligns reconstructed 3D scenes with physical constraints
through verifiable feedback. Given an initial SAM3D reconstruction with artifacts such as floating
objects and inter-object penetration, we construct a multimodal relational scene graph from object
states, spatial visual evidence, and pairwise relations. A shared relational encoder provides structure-
aware representations to an actor–critic policy, which iteratively updates object translation, rotation,
and scale. Physics simulation and visual verification provide verifiable rewards for PPO training. The
resulting policy directly refines scenes at test time, reducing penetration and support violations while
producing configurations that remain stable under simulation.