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，以及一个从随时间变化的数据得分中恢复数据分布的逆向过程。本研究中，我们观察到数据得分的随机逆向过程是一个鞅，由此可推导出数据得分的集中界和可选停止定理。进而，我们发现了一种简单方法用于校准任意预训练的DPM，该方法能够降低得分匹配损失，从而提升模型似然的下界。我们针对不同模型参数化形式提供了通用校准指南。此校准方法仅需执行一次，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，以实证验证所提方案的有效性。相关代码已开源至https://github.com/thudzj/Calibrated-DPMs。