Phase 3: LLM-based Generation · ~45 minutes · Python

Flow Matching & Rectified Flows

Diffusion models take 20-50 sampling steps because they walk a curved path from noise to data. Flow matching (Lipman et al., 2023) and rectified flow (Liu et al., 2022) trained straight paths. Straighter paths mean fewer steps mean faster inference. Stable Diffusion 3, Flux.1, and AudioCraft 2 all switched to flow matching in 2024.

Hiring signal: Understanding of flow matching & rectified flows internals

What you will learn

Implement flow matching & rectified flows from scratch
Understand the math and intuition behind the algorithm
Use production libraries for the same task
Ship a reusable artifact

Introduction

Type: Build Languages: Python Prerequisites: Phase 8 · 06 (DDPM), Phase 1 · Calculus Time: ~45 minutes

The Problem

DDPM's reverse process is a 1000-step stochastic walk from N(0, I) back to the data distribution. DDIM collapsed it to 20-50 deterministic steps. You want fewer steps — ideally one. The blocker is that the ODE solving the reverse process is stiff; the path is curved.

If you could train the model such that the path from noise to data was a straight line, a single Euler step from t=1 to t=0 would work. Flow matching builds this directly: define a straight-line interpolation from x_1 ∼ N(0, I) to x_0 ∼ data, train a vector field v_θ(x, t) to match its time derivative, integrate at inference.

Rectified flow (Liu 2022) goes further: iteratively straighten the paths with a reflow procedure that produces a progressively closer-to-linear ODE. After two reflow iterations, a 2-step sampler matches 50-step DDPM quality.

Unlock the full lesson

You've read the first 2 sections. The rest of this lesson covers The Concept, Flow matching vs DDPM — the exact connection, Build It, Pitfalls, Use It, Ship It, Exercises, Key Terms, Production note: Flux.1-schnell is flow matching at its fastest, Further Reading — plus a hands-on lab, quiz, and project artifact.

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Key terms in this lesson

Inference