Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising Score Matching, however, is that it yields poor estimates of the score at low noise levels. This issue is particularly unfavourable for problems in the physical sciences and for Monte Carlo sampling tasks for which the score of the clean original target is known. Intuitively, estimating the score of a slightly noised version of the target should be a simple task in such cases. In this paper, we address this shortcoming and show that it is indeed possible to leverage knowledge of the target score. We present a Target Score Identity and corresponding Target Score Matching regression loss which allows us to obtain score estimates admitting favourable properties at low noise levels.

翻译：去噪分数匹配通过最小化回归损失来估计目标分布加噪版本的分数，并广泛用于训练流行的去噪扩散模型类。然而，去噪分数匹配的一个众所周知局限是，它在低噪声水平下对分数的估计效果较差。这一问题对物理科学领域的问题以及蒙特卡洛采样任务尤为不利，因为在这些场景中，原始干净目标的分数是已知的。直观而言，在此类情况下，估计目标轻微加噪版本的分数应为简单任务。本文针对此缺陷展开研究，证明利用目标分数先验知识确实可行。我们提出目标分数恒等式及相应的目标分数匹配回归损失，从而获得在低噪声水平下具有优良性质的分数估计。