TOSCA: Transport Operators with Set-valued Certified Assembly for Scene-Graph-to-3D Generation

Generating a 3D scene from a scene graph requires selecting plausible arrangements that satisfy its relations. Graph-conditioned generators can produce plausible layouts that leave requested relations unsatisfied, and high average relation accuracy can coexist with many scenes that fail to satisfy the complete graph. To address this problem, we propose Transport Operators with Set-valued Certified Assembly, TOSCA, which integrates geometric checks and corrections into generation through explicit constraint sets called transport sets. These sets retain the range of configurations permitted by each relation, such as the region of relative object positions allowed by close-by. Projection residuals measure deviations from the allowed sets and guide graph attention and geometric corrections in a flow-matching generator, followed by final refinement. Because individually valid relations may conflict when combined, the same formulation also provides infeasibility certificates for difference constraints and objective bounds for fixed affine convex subproblems. Across SG-FRONT room types, TOSCA increases the fraction of requested relations satisfied by generated geometry and lowers rendered-image FID relative to the evaluated full-split baselines. Ablations support retaining transport sets and final refinement, while conflict and editing experiments assess infeasibility detection and preservation of surrounding objects.