Flow Matching from Scratch

Key Insight

DDPM trains a model to undo noise one small, carefully scheduled step at a time; flow matching throws away the schedule and trains a velocity field instead — a model that, given a half-noisy clip and a time, predicts the single straight-line direction pointing back toward clean video. Rectified flow is the variant that makes those paths actually straight, which is why generation needs far fewer sampling steps than the curvy trajectories of older diffusion. Swapping DDPM for rectified flow inside a small video DiT and watching it converge faster makes concrete why nearly every 2024+ model — SD3, Flux, and most frontier video models — trains this way instead.