Large language models (LLMs) have demonstrated significant advancements in reasoning and code generation, but efficiently creating new benchmarks to evaluate these capabilities remains a challenge. Traditional benchmark creation relies on manual human effort, which is expensive and time-consuming. Furthermore, existing benchmarks often contaminate LLM training data, necessitating novel and diverse benchmarks to accurately assess their genuine capabilities. This work introduces InfoSynth, a novel framework for automatically generating and evaluating reasoning benchmarks guided by information-theoretic principles. We propose metrics based on KL-divergence and entropy to quantify benchmark novelty and diversity without relying on costly model evaluations. Building on this framework, we develop an end-to-end pipeline that synthesizes robust Python coding problems from seed datasets using genetic algorithms and iterative code feedback. Our method generates accurate test cases and solutions to new problems 97% of the time, and the synthesized benchmarks consistently exhibit higher difficulty compared to prior works. Moreover, our algorithm provides a method for controlling the novelty/diversity and difficulty of generated problems. InfoSynth offers a scalable, self-verifying pipeline for constructing high-quality, challenging coding benchmarks for LLMs. Project Page: https://ishirgarg.github.io/infosynth_web/