Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into a Gaussian. Samples from the generative model are then obtained by simulating an approximation of the time reversal of this diffusion initialized by Gaussian samples. Recent research has explored adapting diffusion models for sampling and inference tasks. In this paper, we leverage known connections to stochastic control akin to the F\"ollmer drift to extend established neural network approximation results for the F\"ollmer drift to denoising diffusion models and samplers.

翻译：去噪扩散模型是一类生成模型，近年来在多个领域取得了最先进的效果。通过扩散过程向数据中逐步添加噪声，将数据分布转化为高斯分布。生成模型的样本随后通过模拟该扩散过程的时间反转的近似来获得，该过程以高斯样本初始化。近期研究已探索将扩散模型应用于采样和推理任务。本文利用与类似于Föllmer漂移的随机控制之间的已知联系，将针对Föllmer漂移的现有神经网络逼近结果推广至去噪扩散模型与采样器。