Frost
This window pane is a diffusion model running for real: every ice crystal starts as random static and is nudged, step by step, toward the shape of its training data. Press denoise to watch it freeze, drag the slider left to melt it back into noise, or hold on the glass to breathe on it.
each step: x ← (x + βt·score(x)) / √(1−βt) + σt·z, βt = 0.4300
score(x) = ∇ log pt(x): the direction that makes x look more like the training data
Image generators start from pure static and remove a little noise at a time, each step nudging every speck toward something that looks like the training data. This is that process, slowed down.
Real models learn the score with a neural network; here it is computed exactly from the training points, so you can watch the process itself.
Started from frost ferns growing on a window.