Title: Adaptive Graph Denoising with Harmonic Grouping
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Diffusion, Graph Spectrum, Noise Scheduler

Abstract: Diffusion models have become the leading paradigm for generative modeling, yet their effectiveness in graph domains remains constrained by the instability of topological structures under noise. Existing noise schedulers, however, are typically fixed or heuristic, failing to adapt to either diversity across graph datasets or variability within a dataset. We formulate the challenge of graph diffusion scheduling from two perspectives: inter-diversity, referring to differences across graphs, and intra-variability, referring to variations within individual graphs. To address the challenge in an unified manner, we propose ADHaG (Adaptive graph Denoising with Harmonic Grouping), a novel scheduling framework that explicitly addresses these limitations. Each graph is assigned to a group defined by Laplacian, within which we optimize a feature-conditioned schedule that parameterizes the base scheduler. Empirically, ADHaG demonstrates consistent improvements across both molecular and synthetic benchmarks. In particular, on the QM9 dataset, it attains dataset-level performance with respect to chemical validity; moreover, across all synthetic graph datasets, the orbit statistics consistently improve. These results demonstrate that adaptive scheduling can provide a principled approach to capture both inter- and intra-level variation of graphs.