Test-time tree search improves the reasoning capability of large language models under fixed inference budgets. However, existing solution-level MCTS often suffers from local homogenization: once a promising solution pattern is found, subsequent search tends to refine nearby variants rather than explore distinct reasoning paths. This wastes computation on redundant candidates and limits solution-space coverage. To address this problem, we propose Diversity-Aware Reasoning Tree Search (DARTS), a Bayesian tree-search framework that treats reasoning-path diversity as an explicit search objective. DARTS separates expansion into local refinement and orthogonal regeneration, and updates action posteriors using a joint reward over task quality and reasoning-path diversity. On LiveCodeBench and CodeContests, DARTS achieves the best exploration performance and produces more diverse correct solutions. With half the budget, it matches or exceeds the strongest tree-search baseline in four of six settings. On molecular optimization tasks, DARTS improves both optimization quality and structural diversity, suggesting cross-domain transfer.