A Thousand Steps Collapse Into One Line
Last timeDestroying a Picture on Purpose
Two steps of shrinking and adding noise compose into a single step of the same shape, so any point on the path can be reached directly from the picture in one operation.
The forward process as written is a thousand steps run in order. Training needs
examples from the middle of it, and running hundreds of operations to produce one
training example would make the method unusable. It does not have to.
Two steps are one step
Take two consecutive steps and substitute the first into the second. What comes
out has the same shape: some multiple of the original, plus some noise.
- one minus the noise added at this step, so the share of what was there that survives it
- two independent draws of noise, from the two steps being composed
- one draw standing in for both, which is allowed because independent noises combine into a single one
The whole path in one line
Repeat that composition all the way back to the picture itself and the product of
the shrinks is all that remains of the thousand steps.
The lesson stops here
3 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents