To reveal parent-child influence relationships between nodes in a diffusion network, most prior work requires knowledge of node infection time, which is possible only by carefully monitoring the diffusion process. This work investigates how to solve this problem by learning from diffusion results, which contain only the final infection statuses of nodes in each diffusion process and are often more easily accessible in practice. A conditional entropy-based method is presented to infer potential candidate parent nodes for each node in the network. Furthermore, the inference results are able to be refined by identifying and pruning the inferred influence relations that are unlikely to exist in reality. Experimental results on both synthetic and real-world networks verify the effectiveness and efficiency of our approach.