InfiniteDiffusion

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

SIGGRAPH 2026

Alexander Goslin

Independent Researcher

alexander.goslin@gmail.com

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Abstract

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

InfiniteDiffusion

Until now, content generation has faced a fundamental trilemma: infinite extent, stateless generation, and learned realism - pick any two.<br>Diffusion models achieve realism but are bounded.<br>Classical procedural noise is infinite and stateless, but cannot learn.<br>Auto-regressive outpainting allows learned unbounded generation, but requires a shared global state that precludes determinism and random access.

InfiniteDiffusion breaks this trilemma , transforming any diffusion model into an<br>infinite, logically stateless array, indexed only by seed and coordinates, supporting O(1) random access,<br>full determinism, and embarrassing parallelism. It internally uses only a bounded LRU cache as a performance optimization. No persistent or external state.

InfiniteDiffusion achieves this by generalizing MultiDiffusion for infinite or larger-than-memory domains,<br>acting as a drop-in replacement that reformulates the diffusion process as a lazy computation that<br>generates only the region you request, when you request it.

Each image below compares MultiDiffusion (top), which operates over a pre-defined, eagerly-generated, and bounded canvas, with InfiniteDiffusion (bottom), which imposes no such bounds.<br>InfiniteDiffusion introduces little to no quality degradation compared to MultiDiffusion, while providing the benefits of infinite, stateless, and lazy generation.

Vs. Auto-Regression

The only competing paradigm for unbounded or lazy generation is auto-regression, which carries fundamental limitations that InfiniteDiffusion avoids entirely:

Auto-Regression<br>InfiniteDiffusion

Random Access<br>O(n)<br>O(1)

Determinism<br>No; Order-dependent<br>Yes; Order-invariant

Errors<br>Compound<br>No compounding

Parallelization<br>Sequential<br>Embarrassingly parallel

State<br>Global<br>Functionally Stateless

Training-free<br>No<br>Yes

Terrain Diffusion

Terrain Diffusion is the first learned procedural terrain generator. I introduced a technique<br>that enables diffusion models to generate outputs spanning massive dynamic ranges, from -10000m in the Mariana<br>trench to nearly 9000m at Mt Everest, all in one world. But vertical scale alone is not enough. By utilizing a cascade of diffusion models,<br>Terrain Diffusion generates features spanning hundreds of real-world kilometers , with continents spanning millions of square kilometers.<br>Each 1024x1024 relief map of terrain below spans 100km in width. And it runs locally on consumer hardware .

Built on InfiniteDiffusion, Terrain Diffusion inherits all of its properties: It's functionally stateless,<br>trivially integrates into any game engine, and has almost no practical limitations.<br>To demonstrate this, it was shipped as an open-source<br>Minecraft mod<br>with no external dependencies. Worlds can be<br>shared by seed, players can teleport millions of miles instantly, and it runs in multiplayer.<br>It is also demonstrated in Unity, where the player is able to comfortably fly around the world at 3 times orbital velocity on consumer hardware.

Technical Demo (Unity + Minecraft)

(Cinematic) Mod Showcase by AsianHalfSquat

BibTeX

@inproceedings{goslin2026infinitediffusion,<br>author = {Goslin, Alexander},<br>title = {InfiniteDiffusion: Bridging Learned Fidelity and Procedural Utility for Open-World Terrain Generation},<br>booktitle = {Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers},<br>year = {2026},<br>pages = {10 pages},<br>publisher...