The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed covariance moment matching technique and introduce a novel method for learning the diagonal covariance. Unlike traditional data-driven diagonal covariance approximation approaches, our method involves directly regressing the optimal diagonal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency, recall rate and likelihood of commonly used diffusion models.

翻译：概率扩散模型已在多个领域展现出卓越性能。通常，从扩散模型中采样需要使用去噪分布，该分布以高斯分布为特征，其均值通过学习获得，协方差则采用固定或学习得到的形式。本文利用近期提出的协方差矩匹配技术，提出了一种学习对角协方差的新方法。与传统的数据驱动对角协方差近似方法不同，我们的方法通过名为最优协方差匹配（OCM）的新型无偏目标函数，直接回归最优对角解析协方差。该方法可显著降低协方差预测中的近似误差。我们证明了该方法能够大幅提升常用扩散模型的采样效率、召回率与似然度。