Constraining Generative Models: A Survey from the Constraint Programming Perspective

Abstract

Generative models produce long and high probability sequences, yet they often fail to satisfy explicit constraints set by users. Over the past two decades, Constraint Programming (CP) has provided a complementary paradigm: combining generative models with a constraint solver to guarantee feasibility. This survey reviews the main concepts behind these CP-driven hybrid approaches, from enforcing ubiquitous structural rules (e.g., length and patterns) to preventing plagiarism. It synthesizes how learned models can be treated as constraints, compiled structures, or probabilistic factors. We highlight what has remained stable across applications, then discuss how these principles transfer to the Large Language Model era and outline open challenges for controllable and trustworthy generative systems.