<p>Network diffusion underpins diverse phenomena from social contagion to neural dynamics, yet real-world spreading processes often exhibit complex temporal heterogeneity that transcends Markovian assumptions. Here we present a general theoretical framework incorporating node-specific waiting-time distributions through renewal processes, enabling the integration of temporal heterogeneity with network topology. By formulating dynamics in the Laplace domain, we derive closed-form expressions linking local temporal statistics to the network’s spectral properties, yielding analytical bounds on relaxation times, mixing behavior, and sensitivity to temporal perturbations. Our approach provides quantitative criteria predicting how local timing alterations propagate to global dynamics. We validate the framework through numerical experiments and empirical analysis of <i>α</i>-synuclein spreading in mouse brain networks, where Gamma-based temporal kernels significantly outperform memoryless models. This work establishes a unified foundation for studying non-Markovian diffusion, with implications for understanding spreading processes across biological and social systems.</p>