Automatically generating interactive 3D indoor scenes from natural language is crucial for virtual reality, gaming, and embodied AI. However, existing LLM-based approaches often suffer from spatial errors and collisions, in part because common scene representations-raw coordinates or verbose code-are difficult for models to reason about 3D spatial relationships and physical constraints. We propose SpatialGrammar, a domain-specific language that represents gravity-aligned indoor layouts as BEV grid placements with deterministic compilation to valid 3D geometry, enabling verifiable constraint checking. Building on this representation, we develop (1) SG-Agent, a closed-loop system that uses compiler feedback to iteratively refine scenes and enforce collision constraints, and (2) SG-Mini, a 104M-parameter model trained entirely on compiler-validated synthetic data. Across 159 test scenes spanning five scenarios of different complexity, SG-Agent improves spatial fidelity and physical plausibility over prior methods, while SG-Mini performs competitively against larger LLM-based baselines on single-shot generation scenarios.
@article{arxiv.2604.27555,
title = {SpatialGrammar: A Domain-Specific Language for LLM-Based 3D Indoor Scene Generation},
author = {Song Tang and Kaiyong Zhao and Yuliang Li and Qingsong Yan and Penglei Sun and Junyi Zou and Qiang Wang and Xiaowen Chu},
journal= {arXiv preprint arXiv:2604.27555},
year = {2026}
}