Causal Visual–Trajectory Joint Prediction for Surgical Motion Planning

Effective surgical motion planning requires jointly anticipating future visual states and instrument trajectories, together with an explicit causal relationship between the predicted motion plan and the generated visual future. Existing surgical world models typically treat video generation and trajectory prediction as separate objectives or provide limited evidence that predicted trajectories meaningfully affect visual dynamics. To solve this problem, we propose a joint visual–trajectory prediction framework that establishes an explicit trajectory-to-visual pathway through spatially grounded motion conditioning. The framework transforms predicted trajectories into temporally aligned spatial representations and associates them with observed local appearance to guide future visual dynamics. We further introduce a visual–trajectory causal evaluation framework that measures local visual responses at spatial positions and time steps associated with instrument trajectories. Trajectory-Grounded Motion Alignment (TrajAlign) and Trajectory-Grounded Response Gain (TrajGain) characterize the directional consistency and relative strength of these responses, enabling quantitative assessment of how trajectory conditioning influences future visual dynamics. Experiments demonstrate improved trajectory accuracy and visual–trajectory consistency while maintaining competitive visual quality. Controlled response analysis provides quantitative evidence that trajectory conditioning induces directionally consistent changes in local visual motion, making the trajectory–visual relationship both explicit and measurable.