CRePE: Curved Ray Expectation Positional Encoding for Unified-Camera-Controlled Video Generation

Video world models should predict future appearance in a way that remains consistent with 3D scene structure, camera motion, and lens geometry. Existing attention-level camera encodings, however, either describe each token only by its viewing ray---without locating scene content along that ray---or assume pinhole projection, limiting camera control under wide-angle and fisheye lenses. We introduce Curved Ray Expectation Positional Encoding (CRePE), which represents each image token as a depth-aware distribution along its Unified Camera Model (UCM) ray and integrates the expected rotary positional phasor along the curved path this distribution traces when projected into each query view. CRePE is realized through a lightweight Geometric Attention Adapter on a frozen video diffusion transformer, with pseudo radial-distance supervision from a monocular geometry foundation model serving as a stabilizing anchor rather than an inference-time input. CRePE improves camera-control, lens, and orientation fidelity across pinhole, wide-angle, and fisheye settings, and transfers zero-shot to unseen real fisheye and diverse pinhole videos. Through Radial MixForcing, the same positional pathway further accepts externally supplied radial maps, enabling scene-geometry-conditioned generation and source-video motion transfer that follow the supplied geometry more faithfully than dedicated depth-conditioned baselines. CRePE thus offers a compact interface that unifies camera control, implicit 3D scene state, and external geometry control for video world models.