Table2Text systems generate textual output based on structured data utilizing machine learning. These systems are essential for fluent natural language interfaces in tools such as virtual assistants; however, left to generate freely these ML systems often produce misleading or unexpected outputs. GenNI (Generation Negotiation Interface) is an interactive visual system for high-level human-AI collaboration in producing descriptive text. The tool utilizes a deep learning model designed with explicit control states. These controls allow users to globally constrain model generations, without sacrificing the representation power of the deep learning models. The visual interface makes it possible for users to interact with AI systems following a Refine-Forecast paradigm to ensure that the generation system acts in a manner human users find suitable. We report multiple use cases on two experiments that improve over uncontrolled generation approaches, while at the same time providing fine-grained control. A demo and source code are available at https://genni.vizhub.ai.