[2602.05549] Logical Guidance for the Exact Composition of Diffusion Models

Computer Science > Machine Learning arXiv:2602.05549 (cs) [Submitted on 5 Feb 2026 (v1), last revised 23 Mar 2026 (this version, v2)] Title:Logical Guidance for the Exact Composition of Diffusion Models Authors:Francesco Alesiani, Jonathan Warrell, Tanja Bien, Henrik Christiansen, Matheus Ferraz, Mathias Niepert View a PDF of the paper titled Logical Guidance for the Exact Composition of Diffusion Models, by Francesco Alesiani and Jonathan Warrell and Tanja Bien and Henrik Christiansen and Matheus Ferraz and Mathias Niepert View PDF Abstract:We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas can be obtained from guidance signals associated with atomic properties. First, we derive an exact Boolean calculus that provides a sufficient condition for exact logical guidance. Specifically, if a formula admits a circuit representation in which conjunctions combine conditionally independent subformulas and disjunctions combine subformulas that are either conditionally independent or mutually exclusive, exact logical guidance is achievable. In this case, the guidance signal can be computed exactly from atomic scores and posterior probabilities using an efficient recursive algorithm. Moreover, we show that, for commonly encountered classes of ...