Advanced · Generative AI

Flow Matching

Visual diagram · (in preparation) · Math · (in preparation) · Worked example · 3 difficulty levels.

TL;DR. A generative-modeling framework that learns a velocity field transporting samples from noise to data along a chosen probability path.

Technical Definition

A generative-modeling framework that learns a velocity field transporting samples from noise to data along a chosen probability path.

How it works

Flow matching (Lipman et al., 2023) generalizes diffusion by regressing a continuous-time velocity field v_t(x) against a target field implied by a chosen path between noise and data. Rectified Flow picks straight-line paths, giving very few-step samplers. The framework unifies diffusion and continuous normalizing flows, is simpler to train, and powers Stable Diffusion 3, Flux, and many video models.

Related Concepts

• Diffusion Model — A generative model that learns to create data by reversing a gradual noising process, producing high-quality images and audio.
• Consistency Model — A diffusion-derived model trained so any point on a noise trajectory maps to the same clean sample, enabling 1–4 step generation.