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arxiv: 2606.13240 · v1 · pith:3OY62SCQnew · submitted 2026-06-11 · 💻 cs.LG · cs.AI· cs.CV· stat.ME· stat.ML

Towards More General Control of Diffusion Models Using Jeffrey Guidance

Rapha\"el Razafindralambo , R\'emy Sun , Fr\'ed\'eric Precioso , Jes Frellsen , Pierre-Alexandre Mattei This is my paper

Pith reviewed 2026-06-27 07:33 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CVstat.MEstat.ML
keywords diffusion modelsguidance methodsJeffrey conditioninggenerative modelingdistribution controlfairness in AIimage generationFID metric
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The pith

Jeffrey guidance uses Jeffrey's rule of conditioning to update marginal distributions in diffusion models towards a target while preserving conditional structure.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes Jeffrey guidance to extend control of diffusion models at sampling time beyond standard methods. It leverages Jeffrey's rule to adjust marginal distributions to a prescribed target, preserving the conditional structure and only minimally perturbing the joint distribution. This addresses cases where the target is implicit or defined by heuristics. The approach is demonstrated by matching embedding distributions to lower FID scores and enforcing attribute independence for fairness.

Core claim

Jeffrey guidance leverages Jeffrey's rule of conditioning to update marginal distributions towards a prescribed target, preserving the conditional structure and minimally perturbing the joint distribution. This framework extends diffusion-model control to applications beyond what standard guidance can express.

What carries the argument

Jeffrey's rule of conditioning applied at sampling time, which updates marginals to a target distribution while preserving conditionals and minimally perturbing the joint.

If this is right

  • Targeting Inception embeddings as the distribution reduces FID on CIFAR-10 and FFHQ.
  • Updating an unconditional model on CelebA-HQ enforces independence between attributes for fairness.
  • Jeffrey guidance works for targets defined through sampling rules or heuristic energy functions.
  • It provides control in cases beyond simple conditional sampling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Sequential applications of the rule could allow enforcing multiple marginal constraints simultaneously.
  • The method might apply to other score-based or flow-based generative models.
  • Exploring targets like class-conditional distributions or style embeddings could expand its use cases.

Load-bearing premise

That applying Jeffrey's conditioning rule during the sampling process of diffusion models yields valid samples without breaking the noise schedule or introducing unaccounted shifts.

What would settle it

If generated samples under Jeffrey guidance do not match the target marginal distribution or if the conditional distributions between variables change unexpectedly compared to the original model.

Figures

Figures reproduced from arXiv: 2606.13240 by Fr\'ed\'eric Precioso, Jes Frellsen, Pierre-Alexandre Mattei, Rapha\"el Razafindralambo, R\'emy Sun.

Figure 1
Figure 1. Figure 1: Overview of Jeffrey guidance. While classifier guidance targets a single class, our method generalizes this and provides a distributional guidance framework that updates p(y) toward a target p ⋆ (y), with a correction term added at each diffusion step. This marginal-based framework success￾fully applies to various tasks, including embedding distribution matching and fairness objectives. Beyond standard gui… view at source ↗
Figure 2
Figure 2. Figure 2: FID as a function of the guidance scale λ for different values of δ. On CIFAR-10, guidance improves over the unguided baseline (λ = 0) on both train and test sets for appropriate choices of (λ, δ). We observe that larger values of δ, corresponding to guidance applied earlier in the diffusion process through xb0, require smaller guidance scales to remain stable, whereas smaller δ allows for stronger guidanc… view at source ↗
Figure 3
Figure 3. Figure 3: PCA projection of Inception embeddings on FFHQ. Guided samples (λ = 30.0, δ = 10) exhibit a closer alignment with the test distribution, as visible from the overall shape of the embedding distribution. See Appendix [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of guidance for gender parity. Jeffrey guidance selec￾tively modifies samples (highlighted in red) leaving the most confident samples essentially unchanged, while standard guidance modifies a lot more samples. More samples are available in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Decorrelation of Male and Young: ef￾fect of λ ∈ {0.0, 0.3, 0.5} (from top to bottom) on samples. We highlight in red the transformed samples. The guidance modifies the joint distribu￾tion and, in particular, increases the probability of ym = 0 and yy = 0. More details in Fig.E14 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FID as a function of the guidance scale λ for different values of δ, with 95% confidence intervals. In addition to the mean FID values reported in [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: CIFAR-10 FID as a function of the guidance scale λ for different values of δ using ancestral sampling with guidance. In this case, guidance also improves the FID on the test set, although the gap is not substantial. D.3 2D PCA embedding space: contour plot We display in [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: PCA projection of Inception embeddings on FFHQ. Guided samples (λ = 30.0, δ = 10) exhibit a closer alignment with the test distribution, as visible from the overall shape of the embedding distribution and a reduced distance between empirical and reference means [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Top 4 pairs with the largest differences in pixel space between guided and unguided samples [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Top 30 pairs with the largest differences in Inception embedding space between guided [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Top 30 pairs with the largest differences in pixel space between guided and unguided [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Bottom 30 pairs with the largest differences in Inception embedding space between guided [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Correlation between embedding and pixel distances for different numbers of guidance [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Visualization of distribution matching for gender balance. For each guidance strategy, we adopt the best λ from [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
read the original abstract

A key strength of diffusion models lies in their flexibility, since their outputs can be controlled at sampling time through guidance. However, beyond simple cases such as conditional sampling, the target distribution is often left implicit, defined only through a sampling rule or a heuristic energy function. To address this, we propose Jeffrey guidance, a principled framework that extends diffusion-model control to applications beyond what standard guidance can express. It leverages Jeffrey's rule of conditioning to update marginal distributions towards a prescribed target, preserving the conditional structure and minimally perturbing the joint distribution. We first demonstrate Jeffrey guidance by targeting a prescribed embedding distribution. With Inception embeddings as the target, this leads to substantial reductions in FID on both CIFAR-10 and FFHQ. We further apply Jeffrey guidance to fairness on CelebA-HQ, updating an unconditional diffusion model to enforce independence between attributes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper proposes Jeffrey guidance, a framework extending diffusion model control at sampling time via Jeffrey's rule of conditioning. This updates marginal distributions to a prescribed target while preserving conditional structure and minimally perturbing the joint. Demonstrations target Inception embedding distributions (yielding FID reductions on CIFAR-10 and FFHQ) and enforce attribute independence for fairness on CelebA-HQ using an unconditional model.

Significance. If the compatibility with the reverse diffusion process holds, the approach supplies a principled alternative to heuristic guidance or energy-based methods, enabling explicit marginal control for tasks such as distribution matching and fairness constraints. The reported empirical improvements on standard benchmarks indicate potential practical value beyond existing guidance techniques.

major comments (1)
  1. [Abstract / framework description] The central claim requires that Jeffrey's rule updates can be inserted into the denoising trajectory while exactly preserving the pre-trained score function and the fixed noise schedule. The abstract states the method 'minimally perturb[s] the joint distribution' and 'preserv[es] the conditional structure,' but provides no derivation showing that the resulting process remains a valid solution to the reverse diffusion equation or that the marginal update commutes with the time-dependent variance schedule. If the update alters effective drift terms at intermediate t, the generated samples will not correspond to the claimed target marginal.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying a key point about the theoretical grounding of Jeffrey guidance. We address the concern directly below and propose revisions to improve clarity.

read point-by-point responses

  1. Referee: [Abstract / framework description] The central claim requires that Jeffrey's rule updates can be inserted into the denoising trajectory while exactly preserving the pre-trained score function and the fixed noise schedule. The abstract states the method 'minimally perturb[s] the joint distribution' and 'preserv[es] the conditional structure,' but provides no derivation showing that the resulting process remains a valid solution to the reverse diffusion equation or that the marginal update commutes with the time-dependent variance schedule. If the update alters effective drift terms at intermediate t, the generated samples will not correspond to the claimed target marginal.

    Authors: We agree that the abstract is too concise on this point. Section 3 of the manuscript derives the update by applying Jeffrey's rule to the joint at each discrete timestep t, yielding an adjusted mean for the reverse transition kernel while retaining the original variance schedule and the pre-trained score function (which is used only to recover the conditional). Because the rule is applied after the score-based denoising step and the marginal correction is a linear shift in the mean, it does not alter the drift coefficients of the underlying SDE; the resulting process therefore remains a valid reverse diffusion trajectory whose marginal at t=0 matches the prescribed target. We will revise the abstract and add an explicit remark in Section 3 confirming that the update commutes with the fixed noise schedule. The reported FID improvements and fairness metrics are consistent with this analysis, as the generated samples empirically realize the target marginals. revision: partial

Circularity Check

0 steps flagged

No circularity: framework introduced via external rule with independent demonstrations

full rationale

The visible abstract and description introduce Jeffrey guidance by direct application of an external conditioning rule (Jeffrey's rule) to update marginals in diffusion sampling. No equations, fitted parameters, or self-citations are shown that would make any claimed prediction or result equivalent to its inputs by construction. The FID reductions and fairness application are presented as empirical outcomes of the method rather than tautological renamings or forced fits. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.1-grok · 5705 in / 1023 out tokens · 14270 ms · 2026-06-27T07:33:05.552257+00:00 · methodology

discussion (0)

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