Low-Rank Few-Shot Node Classification by Node-Level Graph Diffusion

In this paper, we propose a novel node-level graph diffusion method with low-rank feature learning for few-shot node classification (FSNC), termed Low-Rank Few-Shot Graph Diffusion Model or LR-FGDM. LR-FGDM first employs a novel Few-Shot Graph Diffusion Model (FGDM) as a node-level graph generative method to generate an augmented graph with an enlarged support set, then performs lowrank transductive classification to obtain the few-shot node classification results. Our graph diffusion model, FGDM, comprises two components, the Hierarchical Graph Autoencoder (HGAE) with an efficient hierarchical edge reconstruction method and a new prototypical regularization, and the Latent Diffusion Model (LDM). The low-rank regularization is robust to the noise inherently introduced by the diffusion model and empirically inspired by the Low Frequency Property. We also provide a strong theoretical guarantee justifying the low-rank regularization for the transductive classification in few-shot learning. To further enhance the performance of LR-FGDM, we introduce LRA-LR-FGDM with a novel efficient LR-Attention layer, or the LRA layer, which applies self-attention to the output of the LR-FGDM encoder. The LRA layer further reduces the kernel complexity of LR-FGDM and contributes to a tighter generalization bound, leading to improved performance. Extensive experimental results evidence the effectiveness of LR-FGDM for few-shot node classification, which outperforms the current state-ofthe-art. The code of the LR-FGDM is available at https://github.com/ Statistical-Deep-Learning/LR-FGDM . Published as a conference paper at ICLR 2026 despite known issues of training instability and poor distributional matching (Dhariwal & Nichol, 2021) . In this work, we propose a novel node-level graph diffusion method with low-rank feature learning for FSNC, termed Low-Rank Few-Shot Graph Diffusion Model or LR-FGDM. LR-FGDM employs a novel Few-Shot Graph Diffusion Model (FGDM) to generate an augmented graph with an enlarged support set. The FGDM in LR-FGDM consists of two components, including the Hierarchical Graph Autoencoder (HGAE) with an efficient hierarchical edge reconstruction method and the Latent Diffusion Model (LDM). The HGAE learns compact latent node features for LDM by incorporating a prototypical regularization to encourage semantic structure in the latent space. The hierarchical edge reconstruction method enables efficient reconstruction of the edges connecting to a node from the latent space in a hierarchical manner to avoid the quadratic complexity in edge reconstruction of the regular GAE (Kipf & Welling, 2016a). Given a FSNC task, the FGDM generates the synthetic graph structure, consisting of the synthetic support nodes and the edges connecting to the original graph. The synthetic graph structure is then incorporated into the original graph, forming an augmented graph with an enlarged support set consisting of the original and synthetic support nodes.