The rapid evolution of visual generative AI has introduced a wide range of intellectual property risks, spanning the unauthorized learning, reproduction, extraction, misuse, and redistribution of protected data and model assets. To address these risks, a growing body of technical defenses has been proposed. However, existing surveys typically organize this literature by lifecycle stage or technical mechanism, which can obscure the protective intent of different methods. This survey presents a two-dimensional taxonomy for IP protection in visual generative models. The primary axis is a Control Logic View, which classifies methods into Information Exposure Control, Generative Behavior Constraint, and Attribution & Accountability according to the risk variable they regulate. The secondary axis distinguishes Data IP from Model IP as cross-cutting asset dimensions. Under this framework, we systematically review protection methods, align evaluation protocols with protection objectives, and discuss open challenges including proactive model-level safeguards, standardized evaluation, robustness against adaptive attacks, and explainable evidence. This survey aims to offer a principled, systematic, and easy-to-follow overview for both new and experienced researchers in visual generative AI IP protection.

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