In plant science, understanding the hierarchical structure of leaf venations is crucial for insights into plant physiology, evolution, and ecology. However, data-driven segmentation methods are hampered by the lack of specialized datasets for hierarchical leaf vein analysis. To address this, we introduce the HierArchical Leaf Vein Segmentation (HALVS) dataset, the first of its kind, containing 5057 high-definition scanned leaf images from three species with 83.8 person-days of human annotations across three vein levels. We propose a novel label-efficient hierarchical segmentation framework combining Partially Supervised Semantic Segmentation (PSSS) and Denoising Diffusion Label Refinement (DDLR). PSSS classifies leaf pixels using primary and secondary vein annotations to generate high-confidence pseudo-labels for the background and tertiary veins, reducing omission errors. DDLR then refines these pseudo-labels, propagating structural priors from sparse veins to accurately recover tertiary veins. This framework significantly improves the integrity and connectivity of tertiary veins at low annotation costs. We also pioneer cross-species learning, training models on easily-annotated species and applying them to difficult ones. Despite challenges, DDLR remarkably enhances segmentation performance across all vein levels, providing an effective solution for complex hierarchical patterns and advancing agricultural research.