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.

翻译：数十年来，程序化世界一直依赖于诸如Perlin噪声等程序化噪声函数构建，这些函数生成速度快且具有无限性，但在真实感和大规模连贯性方面本质上存在局限。相反，扩散模型提供了前所未有的保真度，但通常局限于有边界的画布。我们提出了无限扩散（InfiniteDiffusion），一种无需训练的算法，它重新定义了扩散采样过程，以实现惰性且无界的生成，从而弥合了扩散模型的保真度与程序化噪声不可或缺的特性之间的差距：无缝的无限范围、种子一致性以及恒定时间的随机访问。为展示该方法的实用性，我们提出了地形扩散（Terrain Diffusion）框架，这是一个用于学习程序化地形生成且具有程序化噪声类似接口的框架。我们的框架在消费级GPU上的速度是轨道速度的9倍，能够以交互速率生成逼真的地形。我们集成了一个分层扩散模型堆栈，以耦合行星尺度上下文与局部细节；一个紧凑的拉普拉斯编码，以在地球尺度的动态范围内稳定输出；以及一个开源的无限张量框架，用于对无界张量进行恒定内存的操作。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。