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.

翻译：离散扩散与流匹配模型显著推进了离散结构（包括图）的生成建模。然而，这些模型在加噪过程中的时间依赖性会导致反向过程中的误差累积与传播。这一问题在掩码扩散中尤为突出，是序列建模中已知的局限性，并且如我们所示，它同样影响用于图的离散扩散模型。为解决此问题，我们提出了一种称为迭代去噪的新框架，该框架通过假设跨时间的条件独立性，简化了离散扩散并规避了该问题。此外，我们通过引入一个评判器来增强模型，该评判器在生成过程中，根据实例中元素在数据分布下的似然，选择性地保留或破坏它们。我们的实证评估表明，所提方法在图生成任务中显著优于现有的离散扩散基线模型。