Diffusion network inference is crucial for understanding propagation dynamics and applications in social networks. Recently, inferring networks without timestamps has gained attention due to the high costs of monitoring temporal information and the presence of unknown observation errors. However, existing time-independent methods primarily focus on directly extracting parent-child influence relationships from the data, neglecting to consider the dynamics of the diffusion process. To overcome these limitations, this paper introduces a Tree-based approach for time-independent Diffusion Network Inference (TDNI) based on the independent cascade model. TDNI introduces a tree-based likelihood for the infection status data and develops an optimization strategy to infer the most probable propagation tree for each diffusion process. In addition, TDNI incorporates a post-processing stage that utilizes a proposed likelihood ratio to further filter the remaining candidate edges, thereby ensuring the accuracy of the inference result. Experiments conducted on synthetic and real-world networks show the highly competitive performance of TDNI when compared to other state-of-the-art algorithms. Code is available at https://github.com/cgao-comp/TDNI .