Terrain Diffusion: A Diffusion-Based Successor to Perlin Noise in Infinite, Real-Time Terrain Generation

TL;DR

Terrain Diffusion presents a diffusion-based approach to infinite, seed-consistent terrain generation, addressing the limitations of traditional procedural noise and bounded diffusion. It introduces InfiniteDiffusion to enable unbounded, region-based querying with lazy evaluation and an open Infinite Tensor framework for unbounded inference. A hierarchical stack combines coarse planetary conditioning with high-resolution local detail, stabilized by a signed-square-root transform and Laplacian encodings, enabling coherent, real-time synthesis across planetary scales. Empirical results show real-time latency suitable for streaming and high-fidelity, globally coherent terrain, demonstrated through in-game integration and diverse landscape outputs. The work establishes diffusion models as a practical foundation for procedural worldbuilding at planetary scales, with clear directions for future extension and domain applicability.

Abstract

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, an AI-era successor to Perlin noise 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, enabling seamless, real-time synthesis of boundless landscapes. A hierarchical stack of diffusion models couples planetary context with local detail, while a compact Laplacian encoding stabilizes outputs across Earth-scale dynamic ranges. An open-source infinite-tensor framework supports constant-memory manipulation of unbounded tensors, and few-step consistency distillation enables efficient generation. Together, these components establish diffusion models as a practical foundation for procedural world generation, capable of synthesizing entire planets coherently, controllably, and without limits.

Figures (5)

• Figure 1: A conceptual visualization of InfiniteDiffusion with sliding windows. The user’s query $J_0[R]$ induces a deterministic chain of window queries: computing $J_0[R]$ requires a region $J_1[R_0]$, which in turn requires a region $J_2[R_1]$. Querying $J_2[R_1]$ is inexpensive since it corresponds directly to Gaussian noise.
• Figure 2: Effects of the signed-sqrt transform. Standard deviation become more uniformly distributed with respect to mean elevation, and the range of standard deviations compress.
• Figure 3: Multi-stage elevation generation pipeline. (a) The initial coarse map, which serves as the structural and climatic guide. Can be made by hand or generated procedurally. (b) The refined coarse map, enhanced by our lightweight coarse model to enforce realism. (c) The final 90m elevation map generated by the core latent diffusion model, with InfiniteDiffusion for tiling.
• Figure 4: Twenty generated 1024 by 1024 regions from Terrain Diffusion. Samples cover volcanic islands, high relief mountain systems, and dissected plateaus, illustrating the model’s ability to reproduce diverse landscapes with coherent multi-scale structure. All emerge from one world generated with the same seed as in Figure \ref{['fig:teaser']}. Zoom for details.
• Figure 5: Nine Minecraft scenes generated from Terrain Diffusion using a single fixed biome mapping derived from the model’s climatic outputs. The Distant Horizons mod is used to increase render distance, and Bliss shaders are used to enhance visuals.

Theorems & Definitions (9)

• definition 1: Seed-consistent generative process
• lemma 1: InfiniteDiffusion is seed-consistent
• lemma 2: Algorithm Consistency
• lemma 3: Correctness of a single query
• theorem 1: Seed consistency of the algorithm
• lemma 4: Recursive cost bound
• theorem 2: Uniform bound on cost for window regions
• lemma 5: Parallel window updates at a fixed timestep
• theorem 3: Parallelization of finite query sets