While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute only recently began to yield analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PlanSearch, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PlanSearch generates a diverse set of observations about the problem and uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PlanSearch explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PlanSearch on top of Claude 3.5 Sonnet achieves a pass@200 of 77.0% on LiveCodeBench, outperforming both the best pass-rate achieved without any search (pass@1 = 41.4%) and using standard repeated sampling on top of existing non-search models (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains from search as a function of the diversity over generated ideas.