Large language models (LLMs) are remarkably good at writing code. A particularly valuable case of human-LLM collaboration is code-based UI prototyping, a method for creating interactive prototypes that allows users to view and fully engage with a user interface. We conduct a formative study of GPT Pilot, a leading LLM-generated code-prototyping system, and find that its inflexibility towards change once development has started leads to weaknesses in failure prevention and dynamic planning; it closely resembles the linear workflow of the waterfall model. We introduce DIDUP, a system for code-based UI prototyping that follows an iterative spiral model, which takes changes and iterations that come up during the development process into account. We propose three novel mechanisms for LLM-generated code-prototyping systems: (1) adaptive planning, where plans should be dynamic and reflect changes during implementation, (2) code injection, where the system should write a minimal amount of code and inject it instead of rewriting code so users have a better mental model of the code evolution, and (3) lightweight state management, a simplified version of source control so users can quickly revert to different working states. Together, this enables users to rapidly develop and iterate on prototypes.