The library

How models work

Derive the forward process that destroys a picture, the single training objective that learns to undo one step of it, the sampling loop that runs the destruction backwards, and what guidance, fast samplers and straight-path methods are each changing about that loop

How Noise Becomes a Picture

Destroying a picture with noise is easy and exactly describable. This course derives what it takes to run that destruction backwards, which turns out to be one squared error and a loop.

8 lessons, written and corrected before you arrived. Reading them here needs no account. The first reads the whole way through; the others open and then stop, because a page nobody owns cannot tell who is reading it. Starting the course gives you your own copy, where every idea has problems standing under it and you can ask about any sentence.

Start reading

  1. 01A Thousand Small Steps From a Photograph to StaticThe forward process shrinks the picture slightly and adds a little noise, a thousand times over, and three properties of that one line are what make the whole method possible.
  2. 02A Thousand Steps Collapse Into One Lineopening onlyTwo 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.
  3. 03Five Lines of Training, and One Squared Erroropening onlyThe entire training procedure is to pick a picture, pick a time, add the noise the closed form prescribes, and ask the network which noise it was.
  4. 04One Step Back, a Thousand Timesopening onlyThe reverse of a small forward step has the same simple shape, and the trained network supplies the one quantity needed to point it in the right direction.
  5. 05The Network Is Pointing Uphillopening onlyThe predicted noise turns out to be a scaled gradient of the log density of noised pictures, which is why a denoiser can be used as a generator at all.
  6. 06Overshooting the Condition on Purposeopening onlyA condition handed to the network is honoured too weakly, and the standard fix is to measure its effect on the prediction and then deliberately overshoot it.
  7. 07The Same Model, Twenty Times Fasteropening onlyRemoving the added noise turns the sampler into a fixed path that can be travelled in any number of steps, which is where the twentyfold speedup came from.
  8. 08If the Path Is Yours to Pick, Pick a Lineopening onlyThe path from noise to picture was inherited from a process built for destroying things, and choosing a straight one instead makes every stride along it cheaper.