The complexity and high dimensionality of data are significant factors that contribute to the decreased accuracy and efficiency of traditional classification models. Therefore, we construct a multi-layer graph data classification model based on diffusion interface theory, integrating the power mean Laplacian with the Ginzburg-Landau (GL) energy functional. A fast preconditioned convex differences algorithm is designed to solve the model efficiently. Firstly, we construct multi-layer data structures using methods such as mutual information score (MIS) scoring, aggregate the data using the power mean Laplacian, and establish a multi-layer graph GL energy functional. Then, we transform the original non-convex functional minimization problem into a series of linear systems by combining convex differences with preconditioning techniques. Additionally, we introduce the nonequispaced fast fourier transform (NFFT) fast approximate matrix-vector products to significantly reduce computational complexity. Finally, we compare the proposed model and algorithm with several classical methods on real-world multi-layer datasets, synthetic datasets, and image datasets. The results verify the effectiveness of the proposed method. Numerical experiments demonstrate that the method has a significant advantage in classifying complex, high-dimensional, large-scale data, achieving improved computational efficiency while ensuring classification accuracy.