# InfiniteDiffusion: Bridging Learned Fidelity and Procedural Utility for Open-World Terrain Generation

arXiv: https://arxiv.org/abs/2512.08309 · HTML: https://mlsanity.com/paper/2512.08309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 20 of 20)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [SyncDiffusion: Coherent Montage via Synchronized Joint Diffusions](https://mlsanity.com/paper/2306.05178/) (2023)
- [DemoFusion: Democratising High-Resolution Image Generation With No ](https://mlsanity.com/paper/2311.16973/) (2023)
- [BlockFusion: Expandable 3D Scene Generation using Latent Tri-plane Extrapolation](https://mlsanity.com/paper/2401.17053/) (2024)
- [InfinityGAN: Towards Infinite-Pixel Image Synthesis](https://mlsanity.com/paper/2104.03963/) (2021)
- [Mixture of Diffusers for scene composition and high resolution image generation](https://mlsanity.com/paper/2302.02412/) (2023)
- [WorldGrow: Generating Infinite 3D World](https://mlsanity.com/paper/2510.21682/) (2025)
- [TileGAN: Synthesis of Large-Scale Non-Homogeneous Textures](https://mlsanity.com/paper/1904.12795/) (2019)
- [MESA: Text-Driven Terrain Generation Using Latent Diffusion and Global Copernicus Data](https://mlsanity.com/paper/2504.07210/) (2025)
- [TwinDiffusion: Enhancing Coherence and Efficiency in Panoramic Image Generation with Diffusion Models](https://mlsanity.com/paper/2404.19475/) (2024)
- [A step towards procedural terrain generation with GANs](https://mlsanity.com/paper/1707.03383/) (2017)
- [Terrain Diffusion Network: Climatic-Aware Terrain Generation with Geological Sketch Guidance](https://mlsanity.com/paper/2308.16725/) (2023)
- [One Noise to Rule Them All: Learning a Unified Model of Spatially-Varying Noise Patterns](https://mlsanity.com/paper/2404.16292/) (2024)
- [EarthGen: Generating the World from Top-Down Views](https://mlsanity.com/paper/2409.01491/) (2024)

## Built on by (most cited first, 1 of 1)

- [WorldWeave: Growing Persistent Geometric Worlds for Video Generation](https://mlsanity.com/paper/2609.34221/) (2026)

## Abstract (arXiv)

For decades, procedural worlds have been built on procedural noise functions such as Perlin noise, which are fast and infinite, yet fundamentally limited in realism and large-scale coherence. Conversely, diffusion models offer unprecedented fidelity but remain generally confined to bounded canvases. We introduce InfiniteDiffusion, a training-free algorithm that reformulates diffusion sampling for lazy and unbounded generation, bridging the fidelity of diffusion models with the properties that made procedural noise indispensable: seamless infinite extent, seed-consistency, and constant-time random access. To demonstrate the utility of this approach, we present Terrain Diffusion, a framework for learned procedural terrain generation with a procedural noise-like interface. Our framework outpaces orbital velocity by 9 times on a consumer GPU, enabling realistic terrain generation at interactive rates. We integrate a hierarchical stack of diffusion models to couple planetary context with local detail, a compact Laplacian encoding to stabilize outputs across Earth-scale dynamic ranges, and an open-source infinite-tensor framework for constant-memory manipulation of unbounded tensors. Together, these components position diffusion models as a practical foundation for the next generation of infinite virtual worlds.