Efficiently representing and reconstructing the 3D geometry of biological trees remains a challenging problem in computer vision and graphics. We propose a novel approach for generating realistic tree models from single-view photographs. We cast the 3D information inference problem to a semantic voxel diffusion process, which converts an input image of a tree to a novel Semantic Voxel Structure (SVS) in 3D space. The SVS  encodes the geometric appearance and semantic structural information (e.g., classifying trunks, branches, and leaves), which retains the intricate internal tree features. Tailored to the SVS, we present SVDTree a new hybrid tree modeling approach by combining structure-oriented branch reconstruction and self-organization-based foliage reconstruction. We validate SVDTree by using images from both synthetic and real trees. The comparison results show that our approach can better preserve tree details and achieve more realistic and accurate reconstruction results than previous methods.