mlsanityData to 14 Oct 2026

An Introduction to Flow Matching and Diffusion Models

arXiv 2506.02070 ↗First posted 2 Jun 2025cs.LGcited by 35

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to diffusion and flow-based generative models from first principles. We systematically develop the necessary mathematical background in ordinary and stochastic differential equations and derive the core algorithms of flow matching and denoising diffusion models. We then provide a step-by-step guide to building image and video generators, including training methods, guidance, and architectural design. This course is ideal for machine learning researchers who want to develop a principled understanding of the theory and practice of generative AI.

Key facts. Cited by 35 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 26 of its 51 references that are in the map. First posted on arXiv 2 Jun 2025.

Builds on

26 of 51 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024Flow Matching Guide and Code9 Dec
  2. 2024Generator Matching: Generative modeling with arbitrary Markov processes27 Oct
  3. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design7 Feb
  4. 2023Flow Matching on General Geometries7 Feb
  5. 2022Flow Matching for Generative Modeling6 Oct
  6. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 20

  1. 2017Attention Is All You Needcited by 60,361
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  3. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  5. 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,599
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  7. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  8. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  9. 2022Scalable Diffusion Models with Transformerscited by 6,054
  10. 2022Classifier-Free Diffusion Guidancecited by 5,847
  11. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,181
  12. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
8 more
  1. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  2. 2022eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoiserscited by 931
  3. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 737
  4. 2024Movie Gen: A Cast of Media Foundation Modelscited by 644
  5. 2021ByT5: Towards a token-free future with pre-trained byte-to-byte modelscited by 509
  6. 2022UL2: Unifying Language Learning Paradigmscited by 295
  7. 2020Adversarial score matching and improved sampling for image generationcited by 96
  8. 2024Modeling Caption Diversity in Contrastive Vision-Language Pretrainingcited by 42

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 9; 2026: 26.

35 papers.

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  1. 2025Diffusion Models in Simulation-Based Inference: A Tutorial Reviewcited by 11
  2. 2026DiffusionGemma Technical Reportcited by 11
  3. 2025Guided Flow Policy: Learning from High-Value Actions in Offline Reinforcement Learningcited by 9
  4. 2026HyperDiT: Hyper-Connected Transformers for High-Fidelity Pixel-Space Diffusioncited by 9
  5. 2025Diffusion-Based Impedance Learning for Contact-Rich Manipulation Taskscited by 3
  6. 2025Optimization-Guided Diffusion for Interactive Scene Generationcited by 2
  7. 2026Solving Room Impulse Response Inverse Problems Using Flow Matching with Analytic Wiener Denoisercited by 2
  8. 2026SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularizationcited by 2
  9. 2026Entropy-Regularized Adjoint Matching for Offline Reinforcement Learningcited by 2
  10. 2025Back to the Feature: Explaining Video Classifiers with Video Counterfactual Explanationscited by 1
  11. 2025Max-Entropy Reinforcement Learning with Flow Matching and A Case Study on LQRcited by 1
  12. 2026Reducing Memorisation in Generative Models via Riemannian Bayesian Inferencecited by 1
23 more
  1. 2026Guiding Vector Field Generation via Score-based Diffusion Modelcited by 1
  2. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Modelscited by 1
  3. 2026MarkNull: Model-Agnostic Watermark Removal in AI-Generated Images via On-Manifold Latent Manipulationcited by 1
  4. 2026FlowCPO: A Unified Divergence View of Preference Alignment for Flow Modelscited by 1
  5. 2025Secure and reversible face anonymization with diffusion modelscited by 0
  6. 2025Contact Wasserstein Geodesics for Non-Conservative Schr"odinger Bridgescited by 0
  7. 2025What We Don't C: Manifold Disentanglement for Structured Discoverycited by 0
  8. 2026Can Continuous-Time Diffusion Models Generate and Solve Globally Constrained Discrete Problems? A Study on Sudokucited by 0
  9. 2026Denoising Particle Filters: Learning State Estimation with Single-Step Objectivescited by 0
  10. 2026Towards Faster Language Model Inference Using Mixture-of-Experts Flow Matchingcited by 0
  11. 2026Fashion130K: An E-commerce Fashion Dataset for Outfit Generation with Unified Multi-modal Conditioncited by 0
  12. 2026SF-Flow: Sound field magnitude estimation via flow matching guided by sparse measurementscited by 0
  13. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Modelscited by 0
  14. 2026Flow Control: Steering Vision-Language-Action Models with Simple Real-Time Inputscited by 0
  15. 2026Understanding Latent Flow Models for Tabular Data Synthesis: Targets, Paths, and Samplingcited by 0
  16. 2026Generative Models: Principles, Architectures, and Applicationscited by 0
  17. 2026Uncovering Hidden Leptonic Correlations with Flow Matching and Autoencoderscited by 0
  18. 2026Quantum MeanFlow: single-shot generative sampling on NISQ hardwarecited by 0
  19. 2026Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Taskscited by 0
  20. 2026Double descent is the principle of least actioncited by 0
  21. 2026Time series generation with spectrally aligned latent flow matchingcited by 0
  22. 2026Optimal transport meets speech: a tutorial reviewcited by 0
  23. 2026Universal Local Error and Realized Amplification for the First-Order EDM Predictorcited by 0

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  2. 2025From Navigation to Refinement: Revealing the Two-Stage Nature of Flow-based Diffusion Models through Oracle Velocity
  3. 2023Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians
  4. 2024Step-by-Step Diffusion: An Elementary Tutorial
  5. 2024Exploring Diffusion and Flow Matching Under Generator Matching
  6. 2025Diffusion Models: A Mathematical Introduction
  7. 2025Efficiency vs. Fidelity: A Comparative Analysis of Diffusion Probabilistic Models and Flow Matching on Low-Resource Hardware
  8. 2024Generative Diffusion Modeling: A Practical Handbook