Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis, weather forecasting, and neural surrogates of partial differential equations. Despite their ubiquity it is hard to find an introduction to DDPMs which is simple, comprehensive, clean and clear. The compact explanations necessary in research papers are not able to elucidate all of the different design steps taken to formulate the DDPM and the rationale of the steps that are presented is often omitted to save space. Moreover, the expositions are typically presented from the variational lower bound perspective which is unnecessary and arguably harmful as it obfuscates why the method is working and suggests generalisations that do not perform well in practice. On the other hand, perspectives that take the continuous time-limit are beautiful and general, but they have a high barrier-to-entry as they require background knowledge of stochastic differential equations and probability flow. In this note, we distill down the formulation of the DDPM into six simple steps each of which comes with a clear rationale. We assume that the reader is familiar with fundamental topics in machine learning including basic probabilistic modelling, Gaussian distributions, maximum likelihood estimation, and deep learning.

翻译：去噪扩散概率模型（DDPMs）是一类非常流行的深度生成模型，已成功应用于图像与视频生成、蛋白质与材料合成、天气预报以及偏微分方程的神经替代模型等广泛领域。尽管其应用普遍，但很难找到一篇既简洁、全面又清晰易懂的DDPM入门介绍。研究论文中必不可少的精简说明无法阐明DDPM构建过程中所有不同的设计步骤，而且所呈现步骤背后的原理往往因篇幅限制而被省略。此外，常见的阐述通常从变分下界角度出发，这既无必要，甚至可能有害，因为它模糊了方法有效的根本原因，并暗示了在实践中表现不佳的泛化方向。另一方面，从连续时间极限出发的视角虽然优美且具有普适性，但入门门槛较高，需要具备随机微分方程和概率流的背景知识。在本笔记中，我们将DDPM的构建过程提炼为六个简单步骤，每个步骤均附有清晰的原理解释。我们假设读者熟悉机器学习的基础主题，包括基本概率建模、高斯分布、极大似然估计和深度学习。