Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation

Abstract: Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies between intermediate noisy states lead to error accumulation and propagation during the reverse denoising process - a phenomenon known as compounding denoising errors. To address this problem, we propose a novel framework called Simple Iterative Denoising, which simplifies discrete diffusion and circumvents the issue by assuming conditional independence between intermediate states. Additionally, we enhance our model by incorporating a Critic. During generation, the Critic selectively retains or corrupts elements in an instance based on their likelihood under the data distribution. Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.