Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

翻译：最近，扩散概率模型（DPMs）在多种生成任务中取得了令人瞩目的成果。典型的DPM框架包括一个逐步扩散数据分布的前向过程，以及一个从时间依赖的数据分数中恢复数据分布的反向过程。在本工作中，我们观察到数据分数的随机反向过程是一个鞅，由此可以推导出数据分数的集中界限和可选停止定理。随后，我们发现了一种简单的方法来校准任意预训练的DPM，通过该方法可以降低分数匹配损失，从而增加模型似然的下界。我们针对不同的模型参数化方案提供了通用的校准指南。我们的校准方法只需执行一次，校准后的模型可重复用于采样。我们在多个数据集上进行了实验，以实证验证我们的提议。我们的代码位于 https://github.com/thudzj/Calibrated-DPMs。