SPREAD: Spectral Response Graph Diffusion for Representation Learning

Diffusion models have emerged as a promising paradigm for graph representation learning, which employ progressive perturbation and denoising to learn discriminative representations. However, existing methods rely on uniform or predefined diffusion mechanisms that overlook how heterogeneous spectral distributions influence the diffusion dynamics and recovery capabilities of different frequency components. To address this limitation, we propose SPREAD, a spectral response graph diffusion framework that jointly adapts forward perturbation and reverse reconstruction in accordance with graph spectral properties. In the forward process, we introduce a learnable spectral response function parameterized by Bernstein polynomials to regulate noise intensity across frequency components. In the reverse process, a frequency-aware spectral reconstruction objective weights spectral bands according to the learned spectral response profiles, guiding the recovery of informative frequency components. Theoretical analysis establishes that the proposed model can uniformly approximate arbitrary continuous spectral distribution as the polynomial degree increases. Experiments on node classification benchmarks demonstrate that SPREAD achieves competitive performance compared to baseline methods, with ablation studies further supporting the effectiveness of both proposed mechanisms in SPREAD.