GT2: Directing World Modeling via Geometry-Guided Test-Time Optimization

Video world models offer rich priors for simulating dynamic environments. However, jointly controlling camera and object motions remains challenging because their effects are coupled in the observed video and must be composed consistently in a shared 3D coordinate system. Existing methods typically address this challenge through task-specific training on large-scale videos with detailed camera and object motion annotations, making joint control resource-intensive and difficult to adapt. We propose GT2 (Geometry-Guided Test-Time Optimization), a framework that enables joint camera and object control in pretrained video generators by providing explicit geometric supervision at test time, without additional large-scale training. Specifically, GT2 composes prescribed camera motions and object translations in a shared 3D coordinate system and projects the input scene to construct a coarse preview of their combined visual effects. This geometry-aware preview serves as supervision for test-time optimization, directly steering generation toward the prescribed scene dynamics. Experiments show that GT2 improves joint motion controllability while maintaining high visual quality, reducing camera translation error, camera rotation error, and object control error by approximately 28%, 6%, and 10%, respectively, compared with leading baselines.