This study examines how Large Language Models (LLMs) can reduce biases in text-to-image generation systems by modifying user prompts. We define bias as a model's unfair deviation from population statistics given neutral prompts. Our experiments with Stable Diffusion XL, 3.5 and Flux demonstrate that LLM-modified prompts significantly increase image diversity and reduce bias without the need to change the image generators themselves. While occasionally producing results that diverge from original user intent for elaborate prompts, this approach generally provides more varied interpretations of underspecified requests rather than superficial variations. The method works particularly well for less advanced image generators, though limitations persist for certain contexts like disability representation. All prompts and generated images are available at https://iisys-hof.github.io/llm-prompt-img-gen/