Decision Diagrams are now widely used in model checking as extremely compact representations of state spaces. Many Decision Diagram categories have been developed over the past twenty years based on the same principles. Each one targets a specific domain with its own characteristics. Moreover, each one provides its own definition. It prevents sharing concepts and techniques between these structures. This paper aims to propose a basis for a common Framework for Decision Diagrams. It should help users of this technology to define new Decision Diagram categories thanks to a simple specification mechanism called Controller. This enables the building of efficient Decision Diagrams dedicated to a given problem.