Manifold Alignment for Graph Diffusion

Graph diffusion models are a powerful framework for generating complex structured data. However, existing training objectives such as denoising score matching or squared error minimization operate in a sample-wise manner, which optimize individual samples independently and overlook the underlying manifold geometry of the data distribution. To address this limitation, we propose manifold alignment learning (MAL) for graph diffusion models. MAL aligns the real and generated data distributions by non-parametric kernel density estimation on batch samples, while using a semantically informed embedding space solely to compute kernel similarities. By the MAL, we derive a consistency objective that encourages generated graphs to align with the real data manifold. Consequently, MAL promotes manifold-level distributional alignment at each diffusion step. Extensive experiments on graph benchmarks demonstrate that augmenting baseline graph diffusion models with MAL consistently yields comparable generation quality.