We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away from the manifold. At the same time, we are still able to leverage a nice distribution structure. We derive non-asymptotic bounds on the approximation and generalization errors of the denoising score matching estimate. The rates of convergence are determined by the intrinsic dimension. Furthermore, our bounds remain valid even if we allow the ambient dimension grow polynomially with the sample size.

翻译：我们研究了去噪分数匹配估计的理论性质。我们使用非参数高斯混合模型对观测数据的密度进行建模。我们显著放宽了标准流形假设，允许样本偏离流形。同时，我们仍能利用良好的分布结构。我们推导了去噪分数匹配估计的近似误差与泛化误差的非渐近界。收敛速率由本征维度决定。此外，即使允许环境维度随样本量多项式增长，我们的界仍然成立。