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

arXiv:2606.30053 · stat.ML, cs.LG · Submitted 2026-06-29 · Read on arXiv

Titouan Vayer

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stat.ML, cs.LG

Submitted: 2026-06-29

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Optimal Transport — 21× in this paper · explained in 5 episodes
• Flow Matching — 11× in this paper · explained in 22 episodes
• Generative Modeling — 8× in this paper · explained in 3 episodes
• Fokker-Planck Equation — 4× in this paper · explained in 2 episodes
• Rectified Flow — 3× in this paper · explained in 3 episodes
• Score Function — 3× in this paper · explained in 4 episodes
• Conditional Flow Matching — 1× in this paper · explained in 2 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 4 episodes
• Flow Matching Model — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 3 episodes
• Normalizing Flow — 1× in this paper · explained in 4 episodes
• Normalizing Flows — 1× in this paper · explained in 4 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 6 episodes

Sources

• Flow Matching for Generative Modeling
• Building Normalizing Flows with Stochastic Interpolants
• A survey of the Schr\"odinger problem and some of its connections with optimal transport
• Score-Based Generative Modeling through Stochastic Differential Equations
• Let us Build Bridges: Understanding and Extending Diffusion Generative Models
• Non-Denoising Forward-Time Diffusions
• Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow

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