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Data imputation is a crucial task due to the widespread occurrence of missingdata. Many methods adopt a two-step approach: initially crafting a preliminaryimputation (the "draft") and then refining it to produce the final missing dataimputation result, commonly referred to as "draft-then-refine". In our study,we examine this prevalent strategy through the lens of graph Dirichlet energy.We observe that a basic "draft" imputation tends to decrease the Dirichletenergy. Therefore, a subsequent "refine" step is necessary to restore theoverall energy balance. Existing refinement techniques, such as the GraphConvolutional Network (GCN), often result in further energy reduction. Toaddress this, we introduce a new framework, the Graph Laplacian Pyramid Network(GLPN). GLPN incorporates a U-shaped autoencoder and residual networks tocapture both global and local details effectively. Through extensiveexperiments on multiple real-world datasets, GLPN consistently outperformsstate-of-the-art methods across three different missing data mechanisms. Thecode is available at https://github.com/liguanlue/GLPN.

Data Imputation from the Perspective of Graph Dirichlet Energy