Rectified Flow: Straightening by Retraining

Flow matching joins each noise point to a data point by a straight line, and learns the velocity that moves points along such lines. Here the space has one dimension: the position x runs across the floor, and the time t runs back, from zero to one.

Pair noise and data at random, and the training lines cross each other everywhere. Where two lines cross, the model sees two different velocities at the same place and time, and it learns their average.

The rest of the narration is in the book's Companion.