# Geometry Forcing: Marrying Video Diffusion and 3D Representation for Consistent World Modeling

arXiv: https://arxiv.org/abs/2507.07982 · HTML: https://mlsanity.com/paper/2507.07982/

## Key facts

- Cited by 96 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 83 of its 100 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Placed in

- World models / [Video-generation world models and simulators](https://mlsanity.com/wm/video-generation-world-models-and-simulators/)
- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 83)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [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)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Towards Accurate Generative Models of Video: A New Metric & Challenges](https://mlsanity.com/paper/1812.01717/) (2018)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://mlsanity.com/paper/2108.10869/) (2021)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [GAIA-1: A Generative World Model for Autonomous Driving](https://mlsanity.com/paper/2309.17080/) (2023)
- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)

## Built on by (most cited first, 30 of 96)

- [Spatial Forcing: Implicit Spatial Representation Alignment for Vision-language-action Model](https://mlsanity.com/paper/2510.12276/) (2025)
- [RELIC: Interactive Video World Model with Long-Horizon Memory](https://mlsanity.com/paper/2512.04040/) (2025)
- [What matters for Representation Alignment: Global Information or Spatial Structure?](https://mlsanity.com/paper/2512.10794/) (2025)
- [A Comprehensive Survey on World Models for Embodied AI](https://mlsanity.com/paper/2510.16732/) (2025)
- [Lyra 2.0: Explorable Generative 3D Worlds](https://mlsanity.com/paper/2604.13036/) (2026)
- [FantasyWorld: Geometry-Consistent World Modeling via Unified Video and 3D Prediction](https://mlsanity.com/paper/2509.21657/) (2025)
- [Don't Blind Your VLA: Aligning Visual Representations for OOD Generalization](https://mlsanity.com/paper/2510.25616/) (2025)
- [Gen3R: 3D Scene Generation Meets Feed-Forward Reconstruction](https://mlsanity.com/paper/2601.04090/) (2026)
- [Self-Supervised Flow Matching for Scalable Multi-Modal Synthesis](https://mlsanity.com/paper/2603.06507/) (2026)
- [Improved Baselines with Representation Autoencoders](https://mlsanity.com/paper/2605.18324/) (2026)
- [VGGRPO: Towards World-Consistent Video Generation with 4D Latent Reward](https://mlsanity.com/paper/2603.26599/) (2026)
- [MultiWorld: Scalable Multi-Agent Multi-View Video World Models](https://mlsanity.com/paper/2604.18564/) (2026)
- [S-VAM: Shortcut Video-Action Model by Self-Distilling Geometric and Semantic Foresight](https://mlsanity.com/paper/2603.16195/) (2026)
- [LIVE: Long-horizon Interactive Video World Modeling](https://mlsanity.com/paper/2602.03747/) (2026)
- [AnchorWeave: World-Consistent Video Generation with Retrieved Local Spatial Memories](https://mlsanity.com/paper/2602.14941/) (2026)
- [Representation Alignment for Just Image Transformers is not Easier than You Think](https://mlsanity.com/paper/2603.14366/) (2026)
- [Reinforcement Learning with Inverse Rewards for World Model Post-training](https://mlsanity.com/paper/2509.23958/) (2025)
- [VGGT-World: Transforming VGGT into an Autoregressive Geometry World Model](https://mlsanity.com/paper/2603.12655/) (2026)
- [Geometry-Aware Implicit Memory for Video World Models](https://mlsanity.com/paper/2606.02436/) (2026)
- [EgoForge: Goal-Directed Egocentric World Simulator](https://mlsanity.com/paper/2603.20169/) (2026)
- [Action Images: End-to-End Policy Learning via Multiview Video Generation](https://mlsanity.com/paper/2604.06168/) (2026)
- [World-R1: Reinforcing 3D Constraints for Text-to-Video Generation](https://mlsanity.com/paper/2604.24764/) (2026)
- [Prisma-World: Camera-Controllable Multi-Agent Video World Model](https://mlsanity.com/paper/2606.09507/) (2026)
- [CAMEO: Correspondence-Attention Alignment for Multi-View Diffusion Models](https://mlsanity.com/paper/2512.03045/) (2025)
- [GEM-4D: Geometry-Enhanced Video World Models for Robot Manipulation](https://mlsanity.com/paper/2605.22882/) (2026)
- [Towards Interactive Video World Modeling: Frontiers, Challenges, Benchmarks, and Future Trends](https://mlsanity.com/paper/2606.01164/) (2026)
- [CineScene: Implicit 3D as Effective Scene Representation for Cinematic Video Generation](https://mlsanity.com/paper/2602.06959/) (2026)
- [DreamWorld: Unified World Modeling in Video Generation](https://mlsanity.com/paper/2603.00466/) (2026)
- [VideoWeave: Unlocking Geometric Consistency in Video Generation via Joint Geometry-Video Modeling](https://mlsanity.com/paper/2606.14162/) (2026)
- [Feed-Forward 3D Scene Modeling: A Problem-Driven Perspective](https://mlsanity.com/paper/2604.14025/) (2026)

## Abstract (arXiv)

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge the gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize 3D representations. Our key insight is to guide the model's intermediate representations toward geometry-aware structure by aligning them with features from a geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing geometric features from normalized diffusion representations. We evaluate Geometry Forcing on both camera-view conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods. Project page: https://GeometryForcing.github.io.