# Denoising Diffusion Probabilistic Models in Six Simple Steps

arXiv: https://arxiv.org/abs/2402.04384 · HTML: https://mlsanity.com/paper/2402.04384/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 7 of 7)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)

## Built on by (most cited first, 8 of 8)

- [Influence Functions for Scalable Data Attribution in Diffusion Models](https://mlsanity.com/paper/2410.13850/) (2024)
- [Unlearning or Concealment? A Critical Analysis and Evaluation Metrics for Unlearning in Diffusion Models](https://mlsanity.com/paper/2409.05668/) (2024)
- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models](https://mlsanity.com/paper/2411.18702/) (2024)
- [Modality-Transition Representation Learning for Visible-Infrared Person Re-Identification](https://mlsanity.com/paper/2511.02685/) (2025)
- [Clustering via Self-Supervised Diffusion](https://mlsanity.com/paper/2507.04283/) (2025)
- [Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling](https://mlsanity.com/paper/2508.21255/) (2025)
- [Improved denoising diffusion probabilistic models with efficient non-diagonal covariance modeling](https://mlsanity.com/paper/2608.21972/) (2026)

## Abstract (arXiv)

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.