研究掩码扩散中单步选点的依赖性，揭示选择范围与空间相关性的关键影响。
One-step lowest-variance selection in a Gaussian random-field model motivated by masked diffusion: Total correlation and a square root collision threshold
- 基于高斯场模型，用最小得分位置进行单步选择
- 在平方根尺度下，选中区域的总相关性仍显著且有正下界
- 为掩码扩散中的置信度选择提供理论基准，适合研究生成效率的学者
受掩码离散扩散中置信度引导的并行去掩码启发，我们研究了一个简化的高斯随机场模型中的单步选择。局部相关的非负得分场表示位置不确定性，调度器选择得分最小的K个位置。选中位置间的依赖性通过距离相关的高斯相关模型衡量。该分离提供了可计算的框架，用于量化低分位置几何分布对因子化并行解码依赖代价的影响。我们建立两个互补结果：在保守的亚平方根区域内，所选区块的条件高斯总相关性以概率趋近于零；在平方根尺度上，其相关性保持非可忽略，且具有严格为正的期望下界。合成实验验证了有限尺寸下的预测行为。这些结果为理解预算大小、得分依赖性和空间相关性如何共同影响掩码离散扩散中的单步置信度选择，提供了严格的随机几何基准。
原文摘要 · Abstract (English)
Motivated by confidence-guided parallel unmasking in masked discrete diffusion, we study a single selection step in a stylized Gaussian random-field model. A locally dependent nonnegative score field represents position wise uncertainty, and the scheduler selects the K positions with the smallest scores. Dependence among the selected positions is measured through a distance-dependent Gaussian correlation model. This separation provides a tractable framework for quantifying how the geometry of low-score locations affects the dependence cost of factorized parallel decoding. We establish two complementary results. In a conservative sub-square-root regime, the conditional Gaussian total correlation of the selected block vanishes in probability. At the square-root scale, it remains non-negligible with positive asymptotic probability and admits a strictly positive expectation lower bound. Synthetic experiments support the predicted finite-size behavior. These results provide a rigorous stochastic-geometry baseline for understanding how budget size, score dependence, and spatial correlation jointly shape one-step confidence-based selection in masked discrete diffusion.
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