提出非马尔可夫的单纯形去噪，提升图生成效果
Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation
- 在概率单纯形上进行去噪，避免状态突变
- 在合成与真实图数据上超越现有基线
- 适合需要稳定生成离散结构的研究者
去噪模型如扩散或流匹配近期推动了离散结构的生成建模，但多数方法直接在离散状态空间操作，导致状态突变。我们提出单纯形去噪，一种在概率单纯形上运行的简单而有效的生成框架。核心思想是采用非马尔可夫的加噪方案：对于给定的干净数据点，不同时间的噪声表示条件独立。在保持去噪生成模型理论保证的同时，该方法消除了不必要的约束，从而提升性能并简化公式。实验表明，无约束单纯形去噪在合成与真实世界图数据集上均优于强基线的离散扩散和流匹配模型。结果表明概率单纯形是离散生成建模的有效框架。
原文摘要 · Abstract (English)
Denoising models such as Diffusion or Flow Matching have recently advanced generative modeling for discrete structures, yet most approaches either operate directly in the discrete state space, causing abrupt state changes. We introduce simplex denoising, a simple yet effective generative framework that operates on the probability simplex. The key idea is a non-Markovian noising scheme in which, for a given clean data point, noisy representations at different times are conditionally independent. While preserving the theoretical guarantees of denoising-based generative models, our method removes unnecessary constraints, thereby improving performance and simplifying the formulation. Empirically, \emph{unrestrained simplex denoising} surpasses strong discrete diffusion and flow-matching baselines across synthetic and real-world graph benchmarks. These results highlight the probability simplex as an effective framework for discrete generative modeling.
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