mlsanityData to 7 Oct 2026

Notes on generative modeling: flow matching, diffusion, optimal transport and Schr"odinger bridge

arXiv 2606.30053 ↗First posted 29 Jun 2026stat.ML cs.LGcited by 0

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

Abstract (arXiv)

These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard techniques such as Schr"odinger bridge and flow matching.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 9 of its 17 references that are in the map. First posted on arXiv 29 Jun 2026.

Builds on

9 of 17 references.

Closest ancestors · 2

Same direction, newest first

  1. 2022Flow Matching for Generative Modeling6 Oct
  2. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 7

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  4. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  5. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  6. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Modelscited by 102
  7. 2023Non-Denoising Forward-Time Diffusionscited by 75

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Close in wording, no citation either way

  1. 2026Foundations of Schr"odinger Bridges for Generative Modeling
  2. 2024Exploring Diffusion and Flow Matching Under Generator Matching
  3. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
  4. 2025An Introduction to Flow Matching and Diffusion Models
  5. 2025A Unified Framework for Diffusion Bridge Problems: Flow Matching and Schr"odinger Matching into One
  6. 2024Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective
  7. 2025On the Relation between Rectified Flows and Optimal Transport
  8. 2026Barron Optimal Transport I: Generative Modeling