Critical Iterative Denoising: A Discrete Generative Model Applied to Graphs

Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the time dependencies in the noising process of these models lead to error accumulation and propagation during the backward process. This issue, particularly pronounced in mask diffusion, is a known limitation in sequence modeling and, as we demonstrate, also impacts discrete diffusion models for graphs. To address this problem, we propose a novel framework called Iterative Denoising, which simplifies discrete diffusion and circumvents the issue by assuming conditional independence across time. Additionally, we enhance our model by incorporating a Critic, which during generation 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.