Part 5 · The Maths III: Inside the SOTA Methods
Discrete guidance: sharpening by ratio
Classifier-free guidance ports to discrete diffusion per position, per step. With a conditional and an unconditional prediction for slot ℓ, sample from the renormalized sharpened product:
p̃γ the guided distribution actually sampled · c the conditioning signal · γ the guidance strength: 0 is unguided, larger values push harder toward c at the cost of diversity
Equivalently in logits: ℓ̃ = ℓu + γ(ℓc − ℓu). The dial reads: γ = 0 ignores the condition, γ = 1 is ordinary conditional sampling, γ > 1 exaggerates whatever direction the condition pulls — a token whose conditional-to-unconditional ratio is 2 gets its weight multiplied by 2γ before renormalization. Because tokens are discrete there is no gradient to follow, so the classifier-based variant instead reweights each candidate token by a classifier’s judgment pφ(c | z with that token)γ — same trick whether c is a sentiment, a molecular property, or a DNA motif.