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：近期，扩散概率模型（DPMs）在多种生成任务中取得了显著成果。典型的DPM框架包括一个逐步扩散数据分布的前向过程和一个从时间相关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浓度界和可选停止定理。接着，我们发现了一种校准任意预训练DPM的简单方法，利用该方法可以减小分数匹配损失，从而提升模型似然的下界。我们针对不同的模型参数化方式提供了通用的校准指南。我们的校准方法只需执行一次，得到的模型可重复用于采样。我们在多个数据集上进行了实验，以实证验证我们的方案。我们的代码位于 https://github.com/thudzj/Calibrated-DPMs。