Understanding how information or influence propagates through a network, such as during an epidemic outbreak or the spread of misinformation, is a fundamental yet challenging problem. While prior works have focused on cascade prediction (forecasting future infected nodes), network inference (recovering latent global diffusion graphs), or source localization (identifying diffusion's origin), these approaches do not recover the actual "who-infected-whom" propagation tree for a specific diffusion instance. We introduce DIPT (Deep Identification of Propagation Trees), a probabilistic framework that infers propagation trees from final observed node diffusion states, without knowledge of the underlying diffusion mechanism. DIPT models local influence strengths between nodes and uses a discrete-continuous alternating optimization strategy to jointly learn the diffusion mechanism and infer the propagation structure. Empirical results across eight real-world datasets demonstrate that DIPT consistently outperforms existing approaches in reconstructing propagation trees.