The Gap Between Two Guesses

At every denoising step the model can be run twice: once with the prompt attached, once with it dropped. The two noise predictions disagree, and that disagreement is precisely what the prompt contributed. Classifier-free guidance takes the gap between them and scales it up:

$\hat{\varepsilon} = \varepsilon_{\text{uncond}} + s\,\big(\varepsilon_{\text{cond}} - \varepsilon_{\text{uncond}}\big)$

Task: write guided_noise(eps_uncond, eps_cond, scales), returning one guided prediction per entry of scales, in the same order — a list of lists, every number rounded to 4 decimal places.

• eps_uncond and eps_cond are lists of the same length; work elementwise.
• scales may contain any numbers at all. The familiar range of 5 to 10 is a habit of image tools, not a restriction on the arithmetic.

Read the formula at $s = 1$ and it collapses to $\varepsilon_{\text{cond}}$ — the plain conditioned prediction, with no guidance happening at all. Everything people mean by "turning guidance up" lives at $s > 1$, out beyond the conditioned prediction, at a point no single run of the model ever produced.