# Step-by-Step Diffusion: An Elementary Tutorial

arXiv: https://arxiv.org/abs/2406.08929 · HTML: https://mlsanity.com/paper/2406.08929/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- First posted on arXiv 13 Jun 2024.

## Placed in

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

## Built on by (most cited first, 16 of 16)

- [Affordance-based Robot Manipulation with Flow Matching](https://mlsanity.com/paper/2409.01083/) (2024)
- [High-accuracy and dimension-free sampling with diffusions](https://mlsanity.com/paper/2601.10708/) (2026)
- [Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity](https://mlsanity.com/paper/2503.12966/) (2025)
- [Flow Matching based Sequential Recommender Model](https://mlsanity.com/paper/2505.16298/) (2025)
- [Clustering via Self-Supervised Diffusion](https://mlsanity.com/paper/2507.04283/) (2025)
- [Neural Approaches to SAT Solving: Design Choices and Interpretability](https://mlsanity.com/paper/2504.01173/) (2025)
- [Preserve and Personalize: Personalized Text-to-Image Diffusion Models without Distributional Drift](https://mlsanity.com/paper/2505.19519/) (2025)
- [Diffusion-Based Electromagnetic Inverse Design of Scattering Structured Media](https://mlsanity.com/paper/2511.05357/) (2025)
- [FAVE: Flow-based Average Velocity Establishment for Sequential Recommendation](https://mlsanity.com/paper/2604.04427/) (2026)
- [Diffusion Model from Scratch](https://mlsanity.com/paper/2412.10824/) (2024)
- [Curiosity-Diffuser: Curiosity Guide Diffusion Models for Reliability](https://mlsanity.com/paper/2503.14833/) (2025)
- [Personalized Federated Training of Diffusion Models with Privacy Guarantees](https://mlsanity.com/paper/2504.00952/) (2025)
- [What Do You Need for Compositional Generalization in Diffusion Planning?](https://mlsanity.com/paper/2505.18083/) (2025)
- [Cost-Aware Diffusion Active Search](https://mlsanity.com/paper/2602.19538/) (2026)
- [Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments](https://mlsanity.com/paper/2608.29907/) (2026)
- [DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2609.32363/) (2026)

## Abstract (arXiv)

We present an accessible first course on diffusion models and flow matching for machine learning, aimed at a technical audience with no diffusion experience. We try to simplify the mathematical details as much as possible (sometimes heuristically), while retaining enough precision to derive correct algorithms.