"Stack It Up!": 3D Stable Structure Generation from 2D Hand-drawn Sketch

Imagine a child sketching the Eiffel Tower and asking a robot to bring it to life. Today's robot manipulation systems can't act on such sketches directly-they require precise 3D block poses as goals, which in turn demand structural analysis and expert tools like CAD. We present StackItUp, a system that enables non-experts to specify complex 3D structures using only 2D front-view hand-drawn sketches. StackItUp introduces an abstract relation graph to bridge the gap between rough sketches and accurate 3D block arrangements, capturing the symbolic geometric relations (e.g., left-of) and stability patterns (e.g., two-pillar-bridge) while discarding noisy metric details from sketches. It then grounds this graph to 3D poses using compositional diffusion models and iteratively updates it by predicting hidden internal and rear supports-critical for stability but absent from the sketch. Evaluated on sketches of iconic landmarks and modern house designs, StackItUp consistently produces stable, multilevel 3D structures and outperforms all baselines in both stability and visual resemblance.