Source localization is a representative inverse inference task in information propagation, aiming to identify the source node or node set that triggers the propagation results based on the observed information. A primary challenge is quantifying the inherent uncertainty between observed outcomes and potential sources. Although deep generative models have partially mitigated this issue, most existing approaches primarily focus on uncertainty induced by network topology, attempting to learn a direct mapping from propagation outcomes to sources based on network structure, while overlooking the additional uncertainty stemming from the highly stochastic nature of the propagation process. To address this limitation, we propose a Propagation Dynamics aware framework for Source Localization (PDSL), a novel method that integrates a deep generative model with propagation dynamics to approximate the source distribution and explicitly mitigate uncertainty arising from diffusion stochasticity. Moreover, we employ Graph Neural Ordinary Differential Equations to model the continuous dynamics of diffusion processes without relying on a predefined diffusion mechanism. Additionally, a matching mechanism is designed to extract relevant data blocks that enhance source generation reliability. Comprehensive experiments on both synthetic and real-world diffusion datasets demonstrate the superior performance of the proposed framework across diverse application scenarios.