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. We introduce Terrain Diffusion, a generative framework that bridges the fidelity of diffusion models with the properties that made procedural noise indispensable: seamless infinite extent, seed-consistency, and constant-time random access. At its core is InfiniteDiffusion, a novel algorithm for infinite generation that reformulates standard diffusion sampling for unbounded domains. While noise functions remain near-instant, 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, scalable foundation for the next generation of infinite virtual worlds.

翻译：数十年来，程序化世界构建一直依赖于Perlin噪声等程序化噪声函数，这些方法虽具有快速生成与无限扩展的特性，却在真实感与大规模连贯性方面存在本质局限。本文提出地形扩散生成框架，该框架将扩散模型的高保真度与程序化噪声的核心特性——无缝无限延展、种子一致性和常数时间随机访问——相结合。其核心是InfiniteDiffusion算法，该创新算法通过重构标准扩散采样机制实现了无界域生成。虽然噪声函数仍保持近瞬时生成速度，但本框架在消费级GPU上的处理速度达到轨道速度的9倍，实现了交互速率的真实地形生成。我们采用分层堆叠的扩散模型耦合行星尺度上下文与局部细节，通过紧凑拉普拉斯编码稳定地球级动态范围的输出，并开发开源无限张量框架以实现无界张量的常数内存操作。这些组件共同使扩散模型成为新一代无限虚拟世界实用化、可扩展的基础架构。