Semantic Wave Function Collapse: Natural-Language-Guided Constrained World Generation

Natural-language instructions can describe scenes through mandatory requirements, preferences, and contextual information. Conventional Wave Function Collapse (WFC) enforces local pattern compatibility but cannot, by itself, interpret these instructions or guarantee global requirements such as object counts and connectivity. We introduce Semantic-Constrained Probabilistic WFC (SC-PWFC), a compiler-generator-verifier framework that translates language into typed, executable scene specifications. SC-PWFC combines hard constraints, soft preferences, and contextual priors in an explicit probabilistic model. During scene construction, WFC-style propagation enforces local compatibility, global feasibility checks reject impossible partial scenes, and an independent verifier checks completed scenes. The framework also supports constrained completion, localized editing, and explicit handling of ambiguity and infeasibility. Controlled experiments demonstrate more accurate semantic compilation, more efficient constraint-aware generation, improved preference satisfaction and contextual consistency, and reliable preservation of protected content during editing. SC-PWFC thus extends WFC beyond local pattern generation towards language-guided, probabilistic, and verifiable scene synthesis.