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LIT-839: Classifier-Free Diffusion Guidance

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Properties4
StatusActive — read 2026-10-09 (NOTE-603); worth reading here as the paper that makes guidance a combination of two scores from one network: train with the condition dropped at random, then sample with (1 + w)ε(z, c) − wε(z), extrapolating away from the unconditional estimate. Its own analysis is the point for this record: the combination is inspired by Bayes' rule (an implicit classifier p(c|z) ∝ p(z|c)/p(z)) but, because learned scores need not be gradients of anything, it is in general the score of no density and the gradient of no classifier. The evidence is one proof-of-concept on class-conditional ImageNet: the guidance weight trades FID against Inception score as classifier guidance does, best FID at w = 0.1–0.3, best IS at w ≥ 4.
Tagsprobabilistic-modeling, compositionality
Cited as “paper” byNOTE-603 — Classifier-Free Diffusion Guidance
Cited as “source” byTHEORY-611 — Classifier-free guidance extrapolates between a conditional and an unconditional score learned by one network; with exact scores this equals classifier guidance by the classifier the generative model defines through Bayes' rule, but learned scores need not be conservative, so the guided field is in general the gradient of no density and the tilted distribution that motivates guidance is not shown to be what is sampled

Graph View

Jonathan Ho and Tim Salimans (2022), arXiv preprint (short version at the NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications) — ARXIV-2207.12598

Key takeaways

  • The method (Section 3.2, Algorithms 1–2). Train one network on ε(z_λ, c) and, with probability p_uncond, on the null token, so that ε(z_λ) = ε(z_λ, ∅) is learned too. Sample with ε̃(z_λ, c) = (1 + w)ε(z_λ, c) − wε(z_λ). Two forward passes per step; no classifier, no classifier gradients.
  • What it is modelled on, and what it is not (Section 3). Classifier guidance samples approximately from p̃(z|c) ∝ p(z|c)p(c|z)^w. With exact scores, ε* differences give the gradient of an implicit classifier p_i(c|z) ∝ p(z|c)/p(z), and guiding with it gives the same formula. But the learned ε are unconstrained networks, not conservative fields, so ε̃ “is not in general the (scaled) gradient of any classifier”, and no scalar potential need exist for it. The tilted density is the motivation, not a guarantee about what is sampled.
  • The evidence (Section 4, Tables 1–2). Class-conditional ImageNet at 64×64 and 128×128, with architectures and hyperparameters tuned for classifier guidance and used unchanged. Raising w trades FID against Inception score monotonically: at 64×64 with p_uncond = 0.1, FID 1.55 at w = 0.1 rising to 26.22 at w = 4, while IS rises from 66.1 to 260.2. At 128×128, w = 0.3 gives FID 2.43 at T = 256, below ADM-G’s 2.97; at equal network evaluations (T = 128) it does worse. p_uncond = 0.5 is worse than 0.1 or 0.2 along the whole frontier.
  • Its explanation of guidance (Section 5): guidance raises the conditional likelihood of the sample while lowering its unconditional likelihood, the second through a negative score term. Strong guidance saturates colours and cuts diversity, which the authors flag as a possible harm.

The reading (NOTE-603) notes that the text says FID is “monotonically decreasing” with w while its tables show it rising; the anthology’s entry (ANTH-LIT-693) flags the same sentence.

Standing in the record

Filed on 2026-10-09 from the manuscript bibliography of 2026-10-09 (work what-survives-translation) at the owner’s request: the manuscript considered it and dropped it from the final reference list. It is read here on its own merits. See the curation entry of that day.

It is also held in the Anthology of the SOTA as ANTH-LIT-693, read there for the guidance weight as a practice and for what it does to FID and Inception score. The second question here, per ADR-013, is the reading on this record’s terms: what the combination of scores is as a probabilistic object. That is the one-term case of the score addition by which Composable Diffusion (LIT-770) composes concepts, and the paper’s own non-conservativeness argument applies to that sum as well (NOTE-603).

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