Fuzzing is an essential method for finding vulnerabilities. Conventional fuzzing looks across a wide input space, but it can’t handle systems that need intricate and specialized input patterns. Grammar-based fuzzing uses formal grammars to shape the inputs the fuzzer generates. This method is crucial for directing fuzzers to generate complicated inputs that adhere to syntactical requirements. However, existing approaches are biased towards certain input features, leading to significant portions of the solution space being under-explored or ignored. In this paper, we review the state-of-the-art methods, emphasizing the limitations of grammar-based fuzzing, and we provide a first approach for incorporating distribution sampling into fuzzing, accompanied by encouraging first findings. This work can represent a significant step towards achieving comprehensive input space exploration in grammar-based fuzzing, with implications for enhancing the robustness and reliability of the fuzzing targets.