Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more generally, any target distribution whose density is known up to a normalizing constant. The key idea is to consider a forward ``noising'' diffusion initialized at the target distribution which ``transports'' this latter to a normal distribution for long diffusion times. The time-reversal of this process, the ``denoising'' diffusion, thus ``transports'' the normal distribution to the target distribution and can be approximated so as to sample from the target. To accelerate simulation, we show how one can introduce and approximate a Schr\"{o}dinger bridge between these two distributions, i.e. a diffusion which transports the normal to the target in finite time.

翻译：去噪扩散模型是一类新颖的生成模型，近期在机器学习领域极为流行。本文阐述如何利用此类思想从后验分布中采样，更一般地，可从任意密度已知（仅差一个归一化常数）的目标分布中采样。核心思想是考虑一个以目标分布为初始化的正向“加噪”扩散过程，该过程在长扩散时间下将目标分布“传输”至正态分布。该过程的时间反转——即“去噪”扩散——则反过来将正态分布“传输”至目标分布，并可近似用于从目标分布中采样。为加速模拟，我们展示了如何引入并近似这两个分布之间的薛定谔桥，即一种能在有限时间内将正态分布传输至目标分布的扩散过程。