Sparse Training of Discrete Diffusion Models for Graph Generation

Generative models for graphs often encounter scalability challenges due to the inherent need to predict interactions for every node pair. Despite the sparsity often exhibited by real-world graphs, the unpredictable sparsity patterns of their adjacency matrices, stemming from their unordered nature, leads to quadratic computational complexity. In this work, we introduce SparseDiff, a denoising diffusion model for graph generation that is able to exploit sparsity during its training phase. At the core of SparseDiff is a message-passing neural network tailored to predict only a subset of edges during each forward pass. When combined with a sparsity-preserving noise model, this model can efficiently work with edge lists representations of graphs, paving the way for scalability to much larger structures. During the sampling phase, SparseDiff iteratively populates the adjacency matrix from its prior state, ensuring prediction of the full graph while controlling memory utilization. Experimental results show that SparseDiff simultaneously matches state-of-the-art in generation performance on both small and large graphs, highlighting the versatility of our method.

Class-Balancing Diffusion Models

Diffusion-based models have shown the merits of generating high-quality visual data while preserving better diversity in recent studies. However, such observation is only justified with curated data distribution, where the data samples are nicely pre-processed to be uniformly distributed in terms of their labels. In practice, a long-tailed data distribution appears more common and how diffusion models perform on such class-imbalanced data remains unknown. In this work, we first investigate this problem and observe significant degradation in both diversity and fidelity when the diffusion model is trained on datasets with class-imbalanced distributions. Especially in tail classes, the generations largely lose diversity and we observe severe mode-collapse issues. To tackle this problem, we set from the hypothesis that the data distribution is not class-balanced, and propose Class-Balancing Diffusion Models (CBDM) that are trained with a distribution adjustment regularizer as a solution. Experiments show that images generated by CBDM exhibit higher diversity and quality in both quantitative and qualitative ways. Our method benchmarked the generation results on CIFAR100/CIFAR100LT dataset and shows outstanding performance on the downstream recognition task.