VIGOR: Verifiable Industrial Geometry Optimization and Repair in Scene Programs

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.

We study open-vocabulary 3D indoor layout generation, which synthesizes diverse and physically plausible scenes from unlabeled 3D assets using free-form language instructions. Recent methods leverage large language models (LLMs) and vision-language models (VLMs) to generate structured scenes from text. However, most model inter-asset relations implicitly or rely on local pairwise constraints and local optimization. These formulations are poorly aligned with the global, highly non-convex layout space, often yielding locally plausible yet globally inconsistent or physically infeasible scenes. We address this problem with a graph-based intermediate representation that separates semantic coherence from physical feasibility, together with a hybrid search-and-refinement strategy. First, Global Semantic Verification (GSV) represents scenes as structured graphs and enforces semantic constraints through rule-based verification. This explicit validation removes contradictory configurations and produces a globally consistent semantic scaffold. Second, Global Physical Feasibility Search (GPFS) combines evolutionary search for global exploration with gradient-based refinement for local exploitation. It reduces dependence on VLM-proposed initialization and improves robustness in non-convex and discontinuous feasible spaces. Together, GSV and GPFS move layout generation beyond local relational modeling and initialization-sensitive optimization toward globally consistent reasoning and search. Experiments show that our method achieves state-of-the-art performance in open-vocabulary 3D indoor layout generation, improving both semantic consistency and physical plausibility.

Existing indoor layout generators produce globally plausible layouts yet may retain local violations such as collisions, out-of-bounds placements, obstructed openings, and blocked circulation. Most prior work focuses on full-scene synthesis or scene-level optimization, with limited support for identifying responsible objects and locally repairing affected regions. We present Roomer, a reflective repair framework that casts these violations as sparse, object-grounded repair problems. Roomer encodes layouts as RoState'' and uses RoReview'' to bind measured violations to implicated objects. A geometry-conditioned vision-language model planner proposes a structured local edit, while a deterministic solver validates it and generates a finite set of candidate edits when needed. Each candidate is committed only if full-scene verification confirms that it resolves the target violation without new hard violations or broken protected constraints. We train the planner on Roomer-CC, a controlled-corruption dataset that pairs faulty layouts with object-grounded violation evidence and known-feasible inverse StatePatches. Since existing benchmarks rarely assess whether physically valid layouts are usable, we introduce Roomer-Eval to assess distributional quality, physical validity, and practical usability. Experiments show that Roomer repairs residual violations while preserving valid regions, improves physical validity and usability, and transfers across external generators.