Category-Theory-Guided Conditional Diffusion Modeling for Climate-Responsive Architectural Spatial Layout Generation

Achieving robust environmental responsiveness in early stage architectural spatial layout design remains a critical challenge under the imperatives of global carbon neutrality and climate-adaptive building practice. Conventional parametric design and multi-objective optimization approaches suffer from computational inefficiency, inadequate constraint satisfaction, and opaque generative logic when operating in high-dimensional design spaces. This paper presents a mathematically rigorous, climate-responsive spatial layout generation framework that unifies category theory with conditional diffusion modeling. The proposed method formalizes site-specific environmental parameter systems and architectural spatial topologies as two small categories, and establishes structure-preserving environment-to-space mappings via covariant functors; natural transformations are further introduced to characterize morphological transitions across distinct design strategies. A conditional diffusion model (CDM) serves as the generative engine, producing candidate spatial topological configurations subject to environmental parameter conditioning. A three-stage categorical constraint screening mechanism—constructed from groupoid structures and pullback limits—enforces simultaneous compliance with functional adjacency requirements, topological coherence, and multi-criteria environmental performance targets. Extensive experiments across three climatically contrasting sites (Hangzhou, Qingdao, and Lijiang) demonstrate that the framework substantially enhances environmental response performance while preserving spatial topological rationality, achieving competitive generation efficiency and constraint satisfaction relative to conventional parametric optimization baselines. These findings establish that categorical structures can serve as interpretable, mathematically consistent constraint engines within AI-driven generative design pipelines, offering a principled computational paradigm for climate-responsive architectural layout synthesis.