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

arXiv: https://arxiv.org/abs/2605.12938 · HTML: https://mlsanity.com/paper/2605.12938/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Video-generation world models and simulators, one of 11 directions in World models.
- Builds on 33 of its 37 references that are in the map.
- First posted on arXiv 13 May 2026.

## Placed in

- World models / [Video-generation world models and simulators](https://mlsanity.com/wm/video-generation-world-models-and-simulators/)

## Builds on (most cited first, 30 of 33)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [MotionCtrl: A Unified and Flexible Motion Controller for Video Generation](https://mlsanity.com/paper/2312.03641/) (2023)
- [KITTI-360: A Novel Dataset and Benchmarks for Urban Scene Understanding in 2D and 3D](https://mlsanity.com/paper/2109.13410/) (2021)
- [VACE: All-in-One Video Creation and Editing](https://mlsanity.com/paper/2503.07598/) (2025)
- [CameraCtrl: Enabling Camera Control for Text-to-Video Generation](https://mlsanity.com/paper/2404.02101/) (2024)
- [CAT3D: Create Anything in 3D with Multi-View Diffusion Models](https://mlsanity.com/paper/2405.10314/) (2024)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [ControlVideo: Training-free Controllable Text-to-Video Generation](https://mlsanity.com/paper/2305.13077/) (2023)
- [ReCamMaster: Camera-Controlled Generative Rendering from A Single Video](https://mlsanity.com/paper/2503.11647/) (2025)
- [Scene Representation Transformer: Geometry-Free Novel View Synthesis Through Set-Latent Scene Representations](https://mlsanity.com/paper/2111.13152/) (2021)
- [UniDepthV2: Universal Monocular Metric Depth Estimation Made Simpler](https://mlsanity.com/paper/2502.20110/) (2025)
- [ViPE: Video Pose Engine for 3D Geometric Perception](https://mlsanity.com/paper/2508.10934/) (2025)
- [Direct-a-Video: Customized Video Generation with User-Directed Camera Movement and Object Motion](https://mlsanity.com/paper/2402.03162/) (2024)
- [Cameras as Rays: Pose Estimation via Ray Diffusion](https://mlsanity.com/paper/2402.14817/) (2024)
- [Make-Your-Video: Customized Video Generation Using Textual and Structural Guidance](https://mlsanity.com/paper/2306.00943/) (2023)
- [EscherNet: A Generative Model for Scalable View Synthesis](https://mlsanity.com/paper/2402.03908/) (2024)
- [HunyuanWorld 1.0: Generating Immersive, Explorable, and Interactive 3D Worlds from Words or Pixels](https://mlsanity.com/paper/2507.21809/) (2025)
- [GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformers](https://mlsanity.com/paper/2310.10375/) (2023)
- [Ctrl-Adapter: An Efficient and Versatile Framework for Adapting Diverse Controls to Any Diffusion Model](https://mlsanity.com/paper/2404.09967/) (2024)
- [World-consistent Video Diffusion with Explicit 3D Modeling](https://mlsanity.com/paper/2412.01821/) (2024)
- [UniK3D: Universal Camera Monocular 3D Estimation](https://mlsanity.com/paper/2503.16591/) (2025)
- [GeoCalib: Learning Single-image Calibration with Geometric Optimization](https://mlsanity.com/paper/2409.06704/) (2024)
- [YoNoSplat: You Only Need One Model for Feedforward 3D Gaussian Splatting](https://mlsanity.com/paper/2511.07321/) (2025)
- [Unified Camera Positional Encoding for Controlled Video Generation](https://mlsanity.com/paper/2512.07237/) (2025)
- [Segment Any Motion in Videos](https://mlsanity.com/paper/2503.22268/) (2025)
- [Matrix-3D: Omnidirectional Explorable 3D World Generation](https://mlsanity.com/paper/2508.08086/) (2025)

## Built on by (most cited first, 4 of 4)

- [SCoPE: Sightline-Coordinate Positional Encoding for Video Diffusion Transformers](https://mlsanity.com/paper/2606.27345/) (2026)
- [MeRoPE: Metric Rotary Position Embedding for Camera-Controlled Video Generation](https://mlsanity.com/paper/2609.01252/) (2026)
- [G-ray: Ray-Level Relative Geometric Position Encoding in Multi-View Vision Transformers under Camera Heterogeneity](https://mlsanity.com/paper/2609.15018/) (2026)
- [GAD: Geometry Attention Distillation for Consistent Video Generation](https://mlsanity.com/paper/2610.18779/) (2026)

## Abstract (arXiv)

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.