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

InfiniteDiffusion：架起学习保真度与程序化实用性之间的桥梁，用于开放世界地形生成

SIGGRAPH 2026 | Alexander Goslin | Independent Researcher SIGGRAPH 2026 | Alexander Goslin | 独立研究员

Abstract

摘要

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.

几十年来，程序化世界一直建立在诸如柏林噪声（Perlin noise）等程序化噪声函数之上。这些函数虽然快速且无限，但在真实感和大尺度连贯性方面存在根本性的局限。相反，扩散模型提供了前所未有的保真度，但通常局限于有限的画布。我们引入了 InfiniteDiffusion，这是一种无需训练的算法，它重新构建了用于“惰性”且无界生成的扩散采样过程，将扩散模型的保真度与程序化噪声不可或缺的特性结合起来：无缝的无限扩展性、种子一致性以及常数时间的随机访问。

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.

为了展示这种方法的实用性，我们提出了 Terrain Diffusion，这是一个具有程序化噪声接口的学习型程序化地形生成框架。我们的框架在消费级 GPU 上运行速度超过轨道速度的 9 倍，实现了交互式速率下的真实地形生成。我们集成了一个分层扩散模型堆栈，将行星级上下文与局部细节相结合；采用紧凑的拉普拉斯编码来稳定地球尺度动态范围内的输出；并使用开源的无限张量框架来实现对无界张量的常数内存操作。这些组件共同将扩散模型定位为下一代无限虚拟世界的实用基础。

InfiniteDiffusion

Until now, content generation has faced a fundamental trilemma: infinite extent, stateless generation, and learned realism - pick any two. Diffusion models achieve realism but are bounded. Classical procedural noise is infinite and stateless, but cannot learn. 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 infinite, logically stateless array, indexed only by seed and coordinates, supporting O(1) random access, full determinism, and embarrassing parallelism. It internally uses only a bounded LRU cache as a performance optimization. No persistent or external state.

到目前为止，内容生成面临一个根本性的三难困境：无限扩展、无状态生成和学习到的真实感——三者只能取其二。扩散模型实现了真实感，但受到边界限制。经典的程序化噪声是无限且无状态的，但无法学习。自回归外绘（Auto-regressive outpainting）允许学习型的无界生成，但需要共享的全局状态，这排除了确定性和随机访问。InfiniteDiffusion 打破了这一三难困境，将任何扩散模型转换为一个无限的、逻辑上无状态的数组，仅通过种子和坐标进行索引，支持 O(1) 随机访问、完全确定性和极高的并行性。它内部仅使用有限的 LRU 缓存作为性能优化，无需持久化或外部状态。

InfiniteDiffusion achieves this by generalizing MultiDiffusion for infinite or larger-than-memory domains, acting as a drop-in replacement that reformulates the diffusion process as a lazy computation that 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. InfiniteDiffusion introduces little to no quality degradation compared to MultiDiffusion, while providing the benefits of infinite, stateless, and lazy generation.

InfiniteDiffusion 通过将 MultiDiffusion 推广到无限或超出内存的领域来实现这一点，作为一个即插即用的替代方案，将扩散过程重新构建为一种“惰性计算”，即仅在请求时生成所请求的区域。下方的每张图片都对比了 MultiDiffusion（上图，在预定义、预先生成且有界的画布上运行）与 InfiniteDiffusion（下图，不施加此类限制）。与 MultiDiffusion 相比，InfiniteDiffusion 几乎没有质量下降，同时提供了无限、无状态和惰性生成的优势。

Vs. Auto-Regression

与自回归对比

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

对于无界或惰性生成，唯一的竞争范式是自回归，但它存在 InfiniteDiffusion 完全避免的根本性局限：

Feature	Auto-Regression	InfiniteDiffusion
Random Access	O(n)	O(1)
Determinism	No; Order-dependent	Yes; Order-invariant
Errors	Compound	No compounding
Parallelization	Sequential	Embarrassingly parallel
State	Global	Functionally Stateless

特性	自回归	InfiniteDiffusion
随机访问	O(n)	O(1)
确定性	否；依赖顺序	是；顺序无关
误差	累积	无累积
并行化	串行	极高并行
状态	全局	功能上无状态

Terrain Diffusion

Terrain Diffusion is the first learned procedural terrain generator. I introduced a technique that enables diffusion models to generate outputs spanning massive dynamic ranges, from -10000m in the Mariana 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, Terrain Diffusion generates features spanning hundreds of real-world kilometers, with continents spanning millions of square kilometers. Each 1024x1024 relief map of terrain below spans 100km in width. And it runs locally on consumer hardware.

Terrain Diffusion 是第一个学习型的程序化地形生成器。我引入了一种技术，使扩散模型能够生成跨越巨大动态范围的输出，从马里亚纳海沟的 -10000 米到珠穆朗玛峰近 9000 米，全部在同一个世界中。但仅有垂直尺度是不够的。通过利用扩散模型级联，Terrain Diffusion 生成了跨越数百公里现实世界的特征，大陆跨度达数百万平方公里。下方每张 1024x1024 的地形浮雕图宽度均为 100 公里。而且它可以在消费级硬件上本地运行。

Built on InfiniteDiffusion, Terrain Diffusion inherits all of its properties: It’s functionally stateless, trivially integrates into any game engine, and has almost no practical limitations. To demonstrate this, it was shipped as an open-source Minecraft mod with no external dependencies. Worlds can be shared by seed, players can teleport millions of miles instantly, and it runs in multiplayer. 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.

基于 InfiniteDiffusion，Terrain Diffusion 继承了其所有特性：它在功能上是无状态的，可以轻松集成到任何游戏引擎中，并且几乎没有实际限制。为了证明这一点，它被发布为一个无需外部依赖的开源 Minecraft 模组。世界可以通过种子共享，玩家可以瞬间传送数百万英里，并且支持多人游戏。它也在 Unity 中进行了演示，玩家可以在消费级硬件上以 3 倍轨道速度舒适地环游世界。