# Positional Encoding Field

arXiv: https://arxiv.org/abs/2510.20385 · HTML: https://mlsanity.com/paper/2510.20385/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 45 of its 50 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [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)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [pixelSplat: 3D Gaussian Splats from Image Pairs for Scalable Generalizable 3D Reconstruction](https://mlsanity.com/paper/2312.12337/) (2023)
- [DL3DV-10K: A Large-Scale Scene Dataset for Deep Learning-based 3D Vision](https://mlsanity.com/paper/2312.16256/) (2023)
- [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)
- [ViewCrafter: Taming Video Diffusion Models for High-fidelity Novel View Synthesis](https://mlsanity.com/paper/2409.02048/) (2024)
- [SynSin: End-to-end View Synthesis from a Single Image](https://mlsanity.com/paper/1912.08804/) (2019)
- [GEN3C: 3D-Informed World-Consistent Video Generation with Precise Camera Control](https://mlsanity.com/paper/2503.03751/) (2025)
- [ReconFusion: 3D Reconstruction with Diffusion Priors](https://mlsanity.com/paper/2312.02981/) (2023)
- [Single-View View Synthesis with Multiplane Images](https://mlsanity.com/paper/2004.11364/) (2020)
- [LucidDreamer: Domain-free Generation of 3D Gaussian Splatting Scenes](https://mlsanity.com/paper/2311.13384/) (2023)
- [LVSM: A Large View Synthesis Model with Minimal 3D Inductive Bias](https://mlsanity.com/paper/2410.17242/) (2024)
- [Stable Virtual Camera: Generative View Synthesis with Diffusion Models](https://mlsanity.com/paper/2503.14489/) (2025)
- [CAT4D: Create Anything in 4D with Multi-View Video Diffusion Models](https://mlsanity.com/paper/2411.18613/) (2024)
- [DimensionX: Create Any 3D and 4D Scenes from a Single Image with Controllable Video Diffusion](https://mlsanity.com/paper/2411.04928/) (2024)
- [Text2NeRF: Text-Driven 3D Scene Generation with Neural Radiance Fields](https://mlsanity.com/paper/2305.11588/) (2023)

## Built on by (most cited first, 20 of 20)

- [MosaicMem: Hybrid Spatial Memory for Controllable Video World Models](https://mlsanity.com/paper/2603.17117/) (2026)
- [RayRoPE: Projective Ray Positional Encoding for Multi-view Attention](https://mlsanity.com/paper/2601.15275/) (2026)
- [ReDirector: Creating Any-Length Video Retakes with Rotary Camera Encoding](https://mlsanity.com/paper/2511.19827/) (2025)
- [Matrix-Game 3.5: Enhancing Real-Time Streaming Interactive World Models with Patch Memory](https://mlsanity.com/paper/2608.29910/) (2026)
- [SCoPE: Sightline-Coordinate Positional Encoding for Video Diffusion Transformers](https://mlsanity.com/paper/2606.27345/) (2026)
- [OpenWorldLib: A Unified Codebase and Definition of Advanced World Models](https://mlsanity.com/paper/2604.04707/) (2026)
- [ContextDrag: Precise Drag-Based Image Editing via Context-Preserving Token Injection and Position-Aligned Attention](https://mlsanity.com/paper/2512.08477/) (2025)
- [GSCompleter: A Distillation-Free Plugin for Metric-Aware 3D Gaussian Splatting Completion in Seconds](https://mlsanity.com/paper/2604.20155/) (2026)
- [Geometry without Position? When Positional Embeddings Help and Hurt Spatial Reasoning](https://mlsanity.com/paper/2601.22231/) (2026)
- [One View Is Enough: In-the-Wild Monocular Pretraining for Novel View Generation](https://mlsanity.com/paper/2603.23488/) (2026)
- [Token Warping Helps MLLMs Look from Nearby Viewpoints](https://mlsanity.com/paper/2604.02870/) (2026)
- [UniGeo: Unifying Geometric Guidance for Camera-Controllable Image Editing via Video Models](https://mlsanity.com/paper/2604.17565/) (2026)
- [Pose-ICL: 3D-Aware In-Context Learning for Pose-Controllable Subject Customization](https://mlsanity.com/paper/2606.10902/) (2026)
- [RoPEMover: Depth-Aware Object Relocation via Positional Embeddings](https://mlsanity.com/paper/2606.27332/) (2026)
- [MetaView: Monocular Novel View Synthesis with Scale-Aware Implicit Geometry Priors](https://mlsanity.com/paper/2607.12000/) (2026)
- [HRDiT: Training-Free High-Resolution Image Generation with Off-the-Shelf Diffusion Transformer Models](https://mlsanity.com/paper/2608.07003/) (2026)
- [ReX-Shot: Single-Image Rephotography via Geometry- and Camera-Grounded Generation](https://mlsanity.com/paper/2608.18593/) (2026)
- [DirectUV: Image-Conditioned UV Texture Generation with Surface-Aware Positional Encoding](https://mlsanity.com/paper/2609.34651/) (2026)
- [Geometry as Address: Routing Attention to Visual Memory for Long-Horizon Camera-Controlled Video Generation](https://mlsanity.com/paper/2609.34722/) (2026)
- [Texture Space Material Diffusion](https://mlsanity.com/paper/2609.37654/) (2026)

## Abstract (arXiv)

Diffusion Transformers (DiTs) have emerged as the dominant architecture for visual generation, powering state-of-the-art image and video models. By representing images as patch tokens with positional encodings (PEs), DiTs combine Transformer scalability with spatial and temporal inductive biases. In this work, we revisit how DiTs organize visual content and discover that patch tokens exhibit a surprising degree of independence: even when PEs are perturbed, DiTs still produce globally coherent outputs, indicating that spatial coherence is primarily governed by PEs. Motivated by this finding, we introduce the Positional Encoding Field (PE-Field), which extends positional encodings from the 2D plane to a structured 3D field. PE-Field incorporates depth-aware encodings for volumetric reasoning and hierarchical encodings for fine-grained sub-patch control, enabling DiTs to model geometry directly in 3D space. Our PE-Field-augmented DiT achieves state-of-the-art performance on single-image novel view synthesis and generalizes to controllable spatial image editing.