Snapshot hyperspectral imaging systems acquire spectral data cubes through compressed sensing. Recently, diffractive snapshot spectral imaging (DSSI) methods have attracted significant attention. While various optical designs and improvements continue to emerge, research on reconstruction algorithms remains limited. Although numerous networks and deep unfolding methods have been applied on similar tasks, they are not fully compatible with DSSI systems because of their distinct optical encoding mechanism. In this paper, we propose an efficient deep unfolding framework for diffractive systems, termed diffractive deep unfolding (DDU). Specifically, we derive an analytical solution for the data fidelity term in DSSI, ensuring both the efficiency and the effectiveness during the iterative reconstruction process. Given the severely ill-posed nature of the problem, we employ a network-based initialization strategy rather than non-learning-based methods or linear layers, leading to enhanced stability and performance. Our framework demonstrates strong compatibility with existing state-of-the-art (SOTA) models, which effectively address the initialization and prior subproblem. Extensive experiments validate the superiority of the proposed DDU framework, showcasing improved performance while maintaining comparable parameter counts and computational complexity. These results suggest that DDU provides a solid foundation for future unfolding-based methods in DSSI.