Track the Noise, Move the World:3D-Grounded Motion-Consistent Noise for Controllable Video Generation

Diffusion Transformers have recently achieved strong performance in video generation, yet controlling scene geometry under viewpoint changes and camera motion remains challenging. In this work, we revisit the role of positional encoding in video diffusion transformers and show that it provides a useful spatial bias for geometry-aware control. Specifically, if reference tokens are encoded according to their projected locations in the target view, the denoising model is encouraged to retrieve content from position aligned regions of the input video. Building on this observation, we introduce a geometry-aware cross-attention mechanism that enables target video latent tokens to attend to structured context tokens derived from reference images or frames. To establish correspondence between the reference content and the target camera trajectory, we equip the context tokens with a projected positional encoding scheme that combines target-view 2D reprojection with depth-aware disambiguation. At the same time, we preserve the original spatiotemporal positional encoding of the generated video latent, allowing geometric guidance to be injected while maintaining consistency with the video model's native latent structure. The resulting framework provides a simple and effective approach for controllable video generation. It improves spatial controllability in viewpoint-dependent editing tasks, including camera re-trajectory, novel-view video synthesis, and geometry-aware video editing, while preserving the generative prior of the underlying video diffusion model. The code is available at: https://github.com/MTLab/PE-Field.

Video is a rich and scalable source of 3D/4D visual observations, and camera control is a key capability for video generation models to produce geometrically meaningful content. Existing approaches typically learn a mapping from camera motion to video using additional camera modules and paired data. However, such datasets are often limited in scale, diversity, and scene dynamics, which can bias the model toward a narrow output distribution and compromise the strong prior learned by the base model. These limitations motivate a different perspective on camera control. In this paper, we show that camera control need not be modeled as an implicit mapping problem, but can instead be treated as a form of geometric guidance that induces displacements across frames. Specifically, we reformulate camera control into a set of displacement fields and apply them via differentiable resampling of latent features during denoising. Our simple approach achieves effective camera control with minimal degradation across diverse quality metrics compared to fine-tuned baselines. Since our method is applicable to most video diffusion models without training, it can also serve as a probe to study the camera control capabilities of base models. Using this probe, we identify universal biases shared by representative video models, as well as disparities in their responses to camera control. Finally, we benchmark their performance in multi-view generation, offering insights into their potential for 3D/4D tasks.

Re-rendering an existing video from a novel camera viewpoint requires the output to follow the prescribed camera trajectory while preserving the appearance and dynamics of the original scene across every frame. Existing methods rely on per-frame pose embeddings, noisy point-cloud renderings, or implicit learned correspondences, none of which provides an explicit, temporally continuous link between source and target pixels. We propose Track2View, which conditions a video diffusion transformer on paired 3D point tracks: sparse trajectories of scene points projected into both the source and target camera views. These tracks provide explicit spatiotemporal correspondences that are temporally continuous by construction, encoding what content should appear where and when. At the core of Track2View is a dual-view track conditioner that transfers visual context from source to target view through parameter-free geometric operations and learned temporal aggregation, ensuring generalization to arbitrary camera trajectories without memorizing specific motions. We further introduce a data curation pipeline that extracts one-to-one track correspondences by running a 3D point tracker on temporally concatenated multi-camera view pairs. On a 400-video benchmark spanning static and dynamic scenes, Track2View achieves state-of-the-art results across visual quality, view synchronization, and camera accuracy, reducing rotation error by 30-65% and translation error by 61-72% relative to leading baselines. Project page is available at this https URL: https://qjizhi.github.io/track2view