通过分层自适应细化搜索，提升复杂SQL生成的准确性。

Text-to-SQL translates natural language questions into executable SQL queries, enabling intuitive database access for non-experts. While large language models achieve strong performance on Text-to-SQL with prompting, they still struggle with complex queries that involve deeply nested logic or multiple clauses. A widely used approach employs SQL skeletons--intermediate representations of query logic--to streamline generation, but existing methods are limited by their reliance on a single structural hypothesis and lack of progressive reasoning. To overcome these limitations, we propose LEAF-SQL, a novel framework that reframes skeleton prediction as a coarse-to-fine tree search process. LEAF-SQL enables systematic exploration of diverse structural hypotheses with adaptive refinement. Several key techniques are employed in LEAF-SQL: (1) a three-level skeleton hierarchy to guide the search, (2) a Skeleton Formulation Agent to generate diverse candidates, and (3) a Skeleton Evaluation Agent to efficiently prune the search space. This integrated design yields skeleton candidates that are both structurally diverse and granularity-adaptive, providing a stronger foundation for the SQL generation. Extensive experiments show that LEAF-SQL consistently improves the performance of various LLM backbones. On the official hidden test set of the challenging BIRD benchmark, our method achieves 71.6 execution accuracy, which outperforms leading search-based and skeleton-based methods, affirming its effectiveness for complex queries.