Robots operating safely in cluttered everyday environments often need to infer scene geometry from partial observations. Methods that detect objects in 2D and reconstruct them independently struggle in such scenes: a missed object is never reconstructed, a merged detection can fuse two objects, and separately reconstructed meshes may overlap or fail to touch their supporting surfaces.

We introduce CODA (Complete Once, Decompose Afterward), a generative model that instead reconstructs the complete scene geometry from a single unsegmented RGB-D image, then separates the surface into the surrounding environment and movable objects. Still, generated scene geometry can drift from the observed partial point cloud.

To reduce this drift, CODA uses two explicit 3D grounding mechanisms to keep reconstructed geometry consistent with observed surfaces while completing unseen regions. Experiments on HomebrewedDB and our custom cluttered-scene dataset show more accurate reconstructions and a higher fraction of objects remaining in place under simulated gravity than both object-first and scene-first baselines.