将渲染图直接注入噪声流，提升视频重拍摄的轨迹控制精度

Video re-shooting re-renders a monocular video of a dynamic scene along a user-specified camera trajectory, and the dominant recipe supplies the target geometry explicitly: per-frame depth lifts the source video into a 4D point cloud, which is rasterized along the trajectory into a point cloud render. Because the render and the source video are both handed to the network as visual conditions, they compete at every denoising step, leaving the model with a trust dilemma --- how much of the render to believe --- which can degrade trajectory control or visual quality on data outside the training distribution. We argue that a render already pixel-aligned with the target view does not need to be supplied as an explicit conditioning stream at all. We propose MANIFOLD4D, which injects the render directly into the initial noise of flow matching, so that generation no longer departs from standard Gaussian noise but from a new noise manifold carrying geometric information, leaving the source video as the only visual condition. The render is thus used exactly once, and the network is never asked to learn how to read it; in subsequent denoising steps the model can focus on the source video. On our DAVIS-Traj benchmark and on the Vista4D evaluation set, MANIFOLD4D attains the best camera-control accuracy on every metric, lowering rotation error by 25% and 27% and translation error by up to 32% over the strongest baseline, while matching it in video fidelity and leading on real-world novel-view photometric quality. In a user study, our method achieves clear advantages in trajectory following and dynamic consistency. The gap widens as the yaw amplitude grows past the training range, and the model still recovers correct dynamic motion from the source video when the render is deliberately corrupted, confirming that the geometric prior guides generation without overriding it.