截断扩散采样器在幂律谱下的匹配界研究

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   arXiv · Statistics Machine Learning

   截断扩散采样器需保留多少方向：幂律谱下的匹配界

   论文研究截断扩散采样器在幂律协方差谱数据上需保留多少方向，在环境维度足够大时针对高斯数据与平滑目标证明了匹配界。截断误差取决于被省略方向的合计 Wiener 增益，与采样器在保留坐标上的精度无关；仅保留信号超过输出噪声水平的方向仍会留下非零误差。结合扩散收敛界得到精确 score 下的充分采样步数复杂度，上界还推广到估计主成分及逐分量高斯混合。

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