  Graph diffusion, which iteratively propagates real-valued substances among
the graph, is used in numerous graph/network-involved applications. However,
releasing diffusion vectors may reveal sensitive linking information in the
data such as transaction information in financial network data. However,
protecting the privacy of graph data is challenging due to its interconnected
nature. This work proposes a novel graph diffusion framework with edge-level
differential privacy guarantees by using noisy diffusion iterates. The
algorithm injects Laplace noise per diffusion iteration and adopts a
degree-based thresholding function to mitigate the high sensitivity induced by
low-degree nodes. Our privacy loss analysis is based on Privacy Amplification
by Iteration (PABI), which to our best knowledge, is the first effort that
analyzes PABI with Laplace noise and provides relevant applications. We also
introduce a novel Infinity-Wasserstein distance tracking method, which tightens
the analysis of privacy leakage and makes PABI more applicable in practice. We
evaluate this framework by applying it to Personalized Pagerank computation for
ranking tasks. Experiments on real-world network data demonstrate the
superiority of our method under stringent privacy conditions.
