# Model as a Game: On Numerical and Spatial Consistency for Generative Games

arXiv: https://arxiv.org/abs/2503.21172 · HTML: https://mlsanity.com/paper/2503.21172/

## Key facts

- Cited by 5 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 37 of its 46 references that are in the map.
- First posted on arXiv 27 Mar 2025.

## 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 37)

- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [T2I-Adapter: Learning Adapters to Dig out More Controllable Ability for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.08453/) (2023)
- [Towards Accurate Generative Models of Video: A New Metric & Challenges](https://mlsanity.com/paper/1812.01717/) (2018)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [VideoPoet: A Large Language Model for Zero-Shot Video Generation](https://mlsanity.com/paper/2312.14125/) (2023)
- [CameraCtrl: Enabling Camera Control for Text-to-Video Generation](https://mlsanity.com/paper/2404.02101/) (2024)
- [Uni-ControlNet: All-in-One Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16322/) (2023)
- [ControlVideo: Training-free Controllable Text-to-Video Generation](https://mlsanity.com/paper/2305.13077/) (2023)
- [Composer: Creative and Controllable Image Synthesis with Composable Conditions](https://mlsanity.com/paper/2302.09778/) (2023)
- [Diffusion Models Are Real-Time Game Engines](https://mlsanity.com/paper/2408.14837/) (2024)
- [TrOCR: Transformer-based Optical Character Recognition with Pre-trained Models](https://mlsanity.com/paper/2109.10282/) (2021)
- [TextDiffuser: Diffusion Models as Text Painters](https://mlsanity.com/paper/2305.10855/) (2023)
- [Direct-a-Video: Customized Video Generation with User-Directed Camera Movement and Object Motion](https://mlsanity.com/paper/2402.03162/) (2024)
- [ControlNeXt: Powerful and Efficient Control for Image and Video Generation](https://mlsanity.com/paper/2408.06070/) (2024)
- [ControlNet++: Improving Conditional Controls with Efficient Consistency Feedback](https://mlsanity.com/paper/2404.07987/) (2024)
- [TextDiffuser-2: Unleashing the Power of Language Models for Text Rendering](https://mlsanity.com/paper/2311.16465/) (2023)
- [GameFactory: Creating New Games with Generative Interactive Videos](https://mlsanity.com/paper/2501.08325/) (2025)
- [GameGen-X: Interactive Open-world Game Video Generation](https://mlsanity.com/paper/2411.00769/) (2024)
- [CoDeF: Content Deformation Fields for Temporally Consistent Video Processing](https://mlsanity.com/paper/2308.07926/) (2023)
- [Learning to Simulate Dynamic Environments with GameGAN](https://mlsanity.com/paper/2005.12126/) (2020)
- [VideoControlNet: A Motion-Guided Video-to-Video Translation Framework by Using Diffusion Model with ControlNet](https://mlsanity.com/paper/2307.14073/) (2023)
- [The Matrix: Infinite-Horizon World Generation with Real-Time Moving Control](https://mlsanity.com/paper/2412.03568/) (2024)
- [World-consistent Video Diffusion with Explicit 3D Modeling](https://mlsanity.com/paper/2412.01821/) (2024)
- [Playable Video Generation](https://mlsanity.com/paper/2101.12195/) (2021)

## Built on by (most cited first, 5 of 5)

- [A Survey of Interactive Generative Video](https://mlsanity.com/paper/2504.21853/) (2025)
- [Simulating the Visual World with Artificial Intelligence: A Roadmap](https://mlsanity.com/paper/2511.08585/) (2025)
- [Towards Generalist Game Players: An Investigation of Foundation Models in the Game Multiverse](https://mlsanity.com/paper/2605.09965/) (2026)
- [AI for Games in the Foundation Model Era](https://mlsanity.com/paper/2609.16679/) (2026)
- [Adapting Vision-Language Models for Evaluating World Models](https://mlsanity.com/paper/2506.17967/) (2025)

## Abstract (arXiv)

Recent advances in generative models have significantly impacted game generation. However, despite producing high-quality graphics and adequately receiving player input, existing models often fail to maintain fundamental game properties such as numerical and spatial consistency. Numerical consistency ensures gameplay mechanics correctly reflect score changes and other quantitative elements, while spatial consistency prevents jarring scene transitions, providing seamless player experiences. In this paper, we revisit the paradigm of generative games to explore what truly constitutes a Model as a Game (MaaG) with a well-developed mechanism. We begin with an empirical study on ``Traveler'', a 2D game created by an LLM featuring minimalist rules yet challenging generative models in maintaining consistency. Based on the DiT architecture, we design two specialized modules: (1) a numerical module that integrates a LogicNet to determine event triggers, with calculations processed externally as conditions for image generation; and (2) a spatial module that maintains a map of explored areas, retrieving location-specific information during generation and linking new observations to ensure continuity. Experiments across three games demonstrate that our integrated modules significantly enhance performance on consistency metrics compared to baselines, while incurring minimal time overhead during inference.