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.
Stochastic segmentation seeks to represent multiple plausible masks for a single image, which is essential in safety- and quality-critical applications such as medical imaging or building defect inspection. Most existing methods introduce stochasticity by injecting continuous latent variables or by iterative denoising trajectories, whose stochastic sources are difficult to search or audit directly. We propose architecture distributions as a new stochastic source for segmentation: instead of sampling a latent variable or noise, we sample a discrete architecture from a learned distribution over operator choices at multiple searchable positions in a segmentation backbone. Each sampled architecture yields one mask through the selected active path, so inference depends on the executed subnet rather than the complete candidate bank. This approach also supports architectural provenance, since each output corresponds to a specific architecture configuration. To reduce collapse toward averaged masks, we train with set-level supervision by matching a set of architecture-sampled predictions to the annotation set using an IoU-based energy-distance surrogate. We further construct the candidate bank with evolutionary search, making the support of the stochastic source optimizable before distribution learning. The proposed method achieves state-of-the-art distribution matching and hypothesis coverage on LIDC-IDRI, and remains effective on two extension tasks. To the best of our knowledge, this is the first work to formulate stochastic segmentation as learning an architecture distribution and realizing output diversity through architecture sampling.