Link prediction (LP) in networks aims at determining future interactions among elements; it is a critical machine-learning tool in different domains, ranging from genomics to social networks to marketing, especially in e-commerce recommender systems. Although many LP techniques have been developed in the prior art, most of them consider only static structures of the underlying networks, rarely incorporating the network's information flow. Exploiting the impact of dynamic streams, such as information diffusion, is still an open research topic for LP. Information diffusion allows nodes to receive information beyond their social circles, which, in turn, can influence the creation of new links. In this work, we analyze the LP effects through two diffusion approaches, susceptible-infected-recovered and independent cascade. As a result, we propose the progressive-diffusion (PD) method for LP based on nodes' propagation dynamics. The proposed model leverages a stochastic discrete-time rumor model centered on each node's propagation dynamics. It presents low-memory and low-processing footprints and is amenable to parallel and distributed processing implementation. Finally, we also introduce an evaluation metric for LP methods considering both the information diffusion capacity and the LP accuracy. Experimental results on a series of benchmarks attest to the proposed method's effectiveness compared with the prior art in both criteria.