Step-by-Step Diffusion: An Elementary Tutorial
On the map: Diffusion models → Diffusion foundations and sampling
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.
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.
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Citing papers per year: 2024: 2; 2025: 9; 2026: 5.
16 papers.
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- 2024Affordance-based Robot Manipulation with Flow Matchingcited by 54
- 2026High-accuracy and dimension-free sampling with diffusionscited by 7
- 2025Optimal Denoising in Score-Based Generative Models: The Role of Data Regularitycited by 4
- 2025Flow Matching based Sequential Recommender Modelcited by 3
- 2025Clustering via Self-Supervised Diffusioncited by 3
- 2025Neural Approaches to SAT Solving: Design Choices and Interpretabilitycited by 2
- 2025Preserve and Personalize: Personalized Text-to-Image Diffusion Models without Distributional Driftcited by 1
- 2025Diffusion-Based Electromagnetic Inverse Design of Scattering Structured Mediacited by 1
- 2026FAVE: Flow-based Average Velocity Establishment for Sequential Recommendationcited by 1
- 2024Diffusion Model from Scratchcited by 0
- 2025Curiosity-Diffuser: Curiosity Guide Diffusion Models for Reliabilitycited by 0
- 2025Personalized Federated Training of Diffusion Models with Privacy Guaranteescited by 0
4 more
- 2025What Do You Need for Compositional Generalization in Diffusion Planning?cited by 0
- 2026Cost-Aware Diffusion Active Searchcited by 0
- 2026Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environmentscited by 0
- 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecastingcited by 0
- 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting26 Sep 2026
- 2026Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments30 Aug 2026
- 2026FAVE: Flow-based Average Velocity Establishment for Sequential Recommendation6 Apr 2026
- 2026Cost-Aware Diffusion Active Search23 Feb 2026
- 2026High-accuracy and dimension-free sampling with diffusions15 Jan 2026
- 2025Diffusion-Based Electromagnetic Inverse Design of Scattering Structured Media7 Nov 2025
- 2025Clustering via Self-Supervised Diffusion6 Jul 2025
- 2025Preserve and Personalize: Personalized Text-to-Image Diffusion Models without Distributional Drift26 May 2025
- 2025What Do You Need for Compositional Generalization in Diffusion Planning?23 May 2025
- 2025Flow Matching based Sequential Recommender Model22 May 2025
- 2025Neural Approaches to SAT Solving: Design Choices and Interpretability1 Apr 2025
- 2025Personalized Federated Training of Diffusion Models with Privacy Guarantees1 Apr 2025
4 more
- 2025Curiosity-Diffuser: Curiosity Guide Diffusion Models for Reliability19 Mar 2025
- 2025Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity17 Mar 2025
- 2024Diffusion Model from Scratch14 Dec 2024
- 2024Affordance-based Robot Manipulation with Flow Matching2 Sep 2024
- 2024Affordance-based Robot Manipulation with Flow Matchingcited by 54
- 2026High-accuracy and dimension-free sampling with diffusionscited by 7
- 2025Optimal Denoising in Score-Based Generative Models: The Role of Data Regularitycited by 4
- 2025Flow Matching based Sequential Recommender Modelcited by 3
- 2025Clustering via Self-Supervised Diffusioncited by 3
- 2025Preserve and Personalize: Personalized Text-to-Image Diffusion Models without Distributional Driftcited by 1
- 2025Diffusion-Based Electromagnetic Inverse Design of Scattering Structured Mediacited by 1
- 2024Diffusion Model from Scratchcited by 0
- 2025Curiosity-Diffuser: Curiosity Guide Diffusion Models for Reliabilitycited by 0
- 2025Personalized Federated Training of Diffusion Models with Privacy Guaranteescited by 0
- 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecastingcited by 0
- 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting26 Sep 2026
- 2026High-accuracy and dimension-free sampling with diffusions15 Jan 2026
- 2025Diffusion-Based Electromagnetic Inverse Design of Scattering Structured Media7 Nov 2025
- 2025Clustering via Self-Supervised Diffusion6 Jul 2025
- 2025Preserve and Personalize: Personalized Text-to-Image Diffusion Models without Distributional Drift26 May 2025
- 2025Flow Matching based Sequential Recommender Model22 May 2025
- 2025Personalized Federated Training of Diffusion Models with Privacy Guarantees1 Apr 2025
- 2025Curiosity-Diffuser: Curiosity Guide Diffusion Models for Reliability19 Mar 2025
- 2025Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity17 Mar 2025
- 2024Diffusion Model from Scratch14 Dec 2024
- 2024Affordance-based Robot Manipulation with Flow Matching2 Sep 2024
- 2026Cost-Aware Diffusion Active Searchcited by 0
- 2026Cost-Aware Diffusion Active Search23 Feb 2026
- 2025Neural Approaches to SAT Solving: Design Choices and Interpretabilitycited by 2
- 2026FAVE: Flow-based Average Velocity Establishment for Sequential Recommendationcited by 1
- 2026Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environmentscited by 0
- 2026Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments30 Aug 2026
- 2026FAVE: Flow-based Average Velocity Establishment for Sequential Recommendation6 Apr 2026
- 2025Neural Approaches to SAT Solving: Design Choices and Interpretability1 Apr 2025
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- 2025An Introduction to Flow Matching and Diffusion Models
- 2025Shortcutting Pre-trained Flow Matching Diffusion Models is Almost Free Lunch
- 2024Multistep Distillation of Diffusion Models via Moment Matching
- 2026Rethinking the Diffusion Model from a Langevin Perspective
- 2025Diffusion Models: A Mathematical Introduction
- 2025On the Design of One-step Diffusion via Shortcutting Flow Paths
- 2025From Navigation to Refinement: Revealing the Two-Stage Nature of Flow-based Diffusion Models through Oracle Velocity
- 2022Diffusion Models: A Comprehensive Survey of Methods and Applications