# High Dimensional Procedural Content Generation

arXiv: https://arxiv.org/abs/2602.18943 · HTML: https://mlsanity.com/paper/2602.18943/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Procedural Content Generation via Machine Learning (PCGML)](https://mlsanity.com/paper/1702.00539/) (2017)
- [Learning Controllable 3D Level Generators](https://mlsanity.com/paper/2206.13623/) (2022)
- [DreamCraft: Text-Guided Generation of Functional 3D Environments in Minecraft](https://mlsanity.com/paper/2404.15538/) (2024)
- [DreamGarden: A Designer Assistant for Growing Games from a Single Prompt](https://mlsanity.com/paper/2410.01791/) (2024)
- [Social Conjuring: Multi-User Runtime Collaboration with AI in Building Virtual 3D Worlds](https://mlsanity.com/paper/2410.00274/) (2024)
- [A Database-Driven Framework for 3D Level Generation with LLMs](https://mlsanity.com/paper/2508.18533/) (2025)

## Abstract (arXiv)

Procedural content generation (PCG) has made substantial progress in shaping static 2D/3D geometry, while most methods treat gameplay mechanics as auxiliary and optimize only over space. We argue that this limits controllability and expressivity, and formally introduce High-Dimensional PCG (HDPCG): a framework that elevates non-geometric gameplay dimensions to first-class coordinates of a joint state space. We instantiate HDPCG along two concrete directions. Direction-Space augments geometry with a discrete layer dimension and validates reachability in 4D (x,y,z,l), enabling unified treatment of 2.5D/3.5D mechanics such as gravity inversion and parallel-world switching. Direction-Time augments geometry with temporal dynamics via time-expanded graphs, capturing action semantics and conflict rules. For each direction, we present three general, practicable algorithms with a shared pipeline of abstract skeleton generation, controlled grounding, high-dimensional validation, and multi-metric evaluation. Large-scale experiments across diverse settings validate the integrity of our problem formulation and the effectiveness of our methods on playability, structure, style, robustness, and efficiency. Beyond quantitative results, Unity-based case studies recreate playable scenarios that accord with our metrics. We hope HDPCG encourages a shift in PCG toward general representations and the generation of gameplay-relevant dimensions beyond geometry, paving the way for controllable, verifiable, and extensible level generation.