  Data imputation is a crucial task due to the widespread occurrence of missing
data. Many methods adopt a two-step approach: initially crafting a preliminary
imputation (the "draft") and then refining it to produce the final missing data
imputation 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 Dirichlet
energy. Therefore, a subsequent "refine" step is necessary to restore the
overall energy balance. Existing refinement techniques, such as the Graph
Convolutional Network (GCN), often result in further energy reduction. To
address this, we introduce a new framework, the Graph Laplacian Pyramid Network
(GLPN). GLPN incorporates a U-shaped autoencoder and residual networks to
capture both global and local details effectively. Through extensive
experiments on multiple real-world datasets, GLPN consistently outperforms
state-of-the-art methods across three different missing data mechanisms. The
code is available at https://github.com/liguanlue/GLPN.
