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REVIEW 4 major objections 5 minor 48 references

Moderating the Generalization of Score-based Generative Model

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that score-based generative models can be made to unlearn unwanted data by steering the score function away from it, beating the retrain-on-filtered-data baseline, which leaves the score almost unchanged.

desk verdict A genuinely new score-based unlearning loss with real empirical results, but the retraining claim is overstated and the mechanism lacks a global guarantee; worth serious review after revisions. read the letter →

arxiv 2412.07229 v2 pith:SBVW6CYS submitted 2024-12-10 cs.LG cs.CV

Wan Jiang , He Wang , Xin Zhang , Dan Guo , Zhaoxin Fan , Yunfeng Diao , Richang Hong This is my paper · ORCID
classification cs.LGcs.CV
keywords score-basedgenerativemodelsdiffusionmachineunlearningscorefunctionunintendedgeneralizationconcepterasurenegativelog-likelihoodimageinpainting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper attempts to solve machine unlearning for score-based generative models (SGMs), where diffusion-style generators can produce content that should have been removed. It finds that the usual gold standard, retraining the model on data with the unwanted content excluded, does not work, because the score function stays almost unchanged and the model still generates the unwanted class or attribute. The paper proposes Moderated Score-based Generative Model (MSGM), which changes the score function during training or fine-tuning so sampling steers away from the Not Suitable For Generation (NSFG) data while remaining faithful to the Suitable For Generation (SFG) data. A sympathetic reader would care because it offers a way to control unintended generalization in diffusion models and suggests that the field's usual unlearning baseline needs rethinking.

What carries the argument

The score function $\nabla_x\log p_t(x)$, the gradient of the log-density of the noisy data field that the reverse SDE follows during generation, carries the argument. MSGM's core mechanism is a per-time unlearning loss on the dot product between the model score $s_\theta(x_f(t),t)$ and the conditional score $\nabla_{x_f(t)}\log p_{0t}(x_f(t)\mid x_f(0))$ of the unwanted data: the orthogonal variant pushes this product to zero and the obtuse variant pushes it below zero, while the total objective $\alpha L_g + (1-\alpha)L_f$ keeps the SFG score-matching term active. This deforms the score field so the stochastic process circumvents the NSFG high-density region rather than merely reweighting the training set.

What would settle it

Train MSGM on the paper's mixture-of-Gaussians setup with the middle component as NSFG, then draw a large batch of samples and estimate the density at that component; if the density does not drop sharply relative to the retrained model, the claim that score redirection suppresses generation probability is not supported.

Watch

Extended reading notes

Core claim

The paper's central claim is that unlearning in score-based generative models must act on the score function, not on the training set. It reports that retraining an SGM on data with the unwanted class removed leaves the learned score $\nabla_x\log p_t(x)$ almost unchanged, so the reverse SDE keeps sampling the unwanted region; this is why the accepted 'Unseen by Re-training' gold standard fails. MSGM instead minimizes a dot-product loss between the model's score and the conditional score of the NSFG data at each diffusion time, either forcing the dot product to zero (Orthogonal-MSGM) or forcing it negative (Obtuse-MSGM), while keeping the standard score-matching loss on SFG data. The claimed effect is that sampling is steered away from the high-density region of unwanted data and toward wanted data, lowering unlearning ratios and raising the negative log-likelihood of NSFG data while preserving visual quality.

Load-bearing premise

The load-bearing assumption is that changing the direction of the model's score relative to the unwanted data's score actually moves generated samples away from that unwanted data; if a score can point away from the unwanted region yet sampling still lands there, the method fails.

Editorial extensions

If this is right

  • A single unlearning objective covers VE SDE, VP SDE, DDPM, and latent diffusion models, so the method is not tied to one architecture.
  • The two variants give a practical choice: Orthogonal-MSGM works best when unwanted and retained classes are separable, while Obtuse-MSGM handles closely overlapping features such as facial attributes.
  • MSGM can unlearn from an already trained model by fine-tuning, avoiding the cost of full retraining.
  • In text-to-image experiments, MSGM removes the target class without needing a pseudo-label replacement, avoiding a known failure mode when the substitute class is semantically similar.
  • The unlearned models transfer zero-shot to inpainting and reconstruction: restored unwanted-content images lose their target semantics, while restored retained-content images keep theirs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because the method's loss operates on score directions, one could read off a continuous suppression angle between the model score and the unwanted-data score; a natural test would be to sweep that angle and measure how quickly the NSFG generation rate falls.
  • Editorial inference: the result that retraining leaves the score nearly unchanged implies that deleting data from an SGM's training set is not the same as deleting it from the model, so deletion certifications based on retraining may need a generation-level test.
  • Editorial inference: the success without pseudo-labels in the text-to-image experiment suggests the approach could extend to concept erasure at scale, where finding a semantically distinct replacement class is often the failure mode.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper addresses machine unlearning in score-based generative models (SGMs). It argues that the standard 'Unseen by Re-training' baseline is ineffective for SGMs because retraining on filtered data leaves the learned score function almost unchanged, and it supports this with a 2D Gaussian toy experiment and with class/attribute forgetting experiments on MNIST, CIFAR-10, STL-10, and CelebA. The authors then propose the Moderated Score-based Generative Model (MSGM), which adds an unlearning loss to the standard score-matching objective: Orthogonal-MSGM minimizes the squared dot product between the model score and the NSFG conditional score, while Obtuse-MSGM minimizes (makes negative) the dot product itself. The final objective is a weighted combination of the SFG score-matching loss and the NSFG unlearning loss. Experiments cover VE SDE, VP SDE, DDPM, and Stable Diffusion, with unconditional and conditional generation, and also report zero-shot inpainting and reconstruction results on the unlearned models.

Significance. If the central claims are validated, the paper would be a useful first step toward unlearning in continuous-time score-based models, offering a simple plug-in loss that is compatible with several diffusion architectures and with pre-trained models. The broad experimental scope, including attribute unlearning on CelebA and concept erasure in Stable Diffusion, is a strength. However, the current manuscript does not yet support the strength of the claims: the toy setup contains an invalid mixture, the 'gold standard does not work' conclusion is partially contradicted by the paper's own unlearning-ratio numbers, the mechanism connecting the local score constraint to reduced generation probability is not established, and the evaluation lacks error bars and a full description of the NLL estimator. These issues are fixable, but they are central to the paper's message.

major comments (4)
  1. [Sec. 3.2, toy mixture definition] The toy data distribution is defined as pdata = 4/5 N((-2,-2), I) + 2/5 N((0,0), I) + 4/5 N((2,2), I). The mixture weights sum to 10/5 = 2, so pdata is not a probability density. This invalidates the synthetic experiment as written and, since this experiment is the primary evidence for the claim that retraining 'does not work,' the conclusion must be re-verified after correcting the weights (e.g., to 0.4, 0.2, 0.4).
  2. [Sec. 3.2 and Tab. 2] The claim that Unseen by Re-training 'does not work' is overstated and is contradicted by the paper's own numbers in Tab. 2: Unseen achieves UR of 1.8% on MNIST digit 3, 2.3% on digit 7, 3.4% on CIFAR-10 automobile, and 10.8% on dog, which are close to several MSGM results (e.g., CIFAR-10 dog: 10.0% for Ort, 11.5% for Obt). The NLL values do show that Df likelihood remains close to Dg (MNIST Df 3.01 vs Dg 3.07), but the paper should state precisely which definition of forgetting is being used and reconcile the low UR with the high NLL. In addition, the 'score function almost unchanged' claim in Sec. 3.2 is supported only by visual inspection of Fig. 1; a quantitative distance between the score functions of Standard and Unseen should be reported.
  3. [Sec. 3.3, Eqs. (7)-(9), and Sec. 4.5, Fig. 8] The central mechanism--that making the model score orthogonal or negatively correlated with the NSFG conditional score at noised Df samples will reduce the probability of generating Df--is not proven and is not obviously implied by the loss. The loss constrains the score only on the forward-noised Df training samples, whereas sampling integrates the score field globally from pure noise. The qualitative results show that Orthogonal-MSGM replaces the forgotten feature with noise (Fig. 4) and reconstructs Df as noisy images (Fig. 8), which is consistent with local score destruction or network collapse rather than a genuine global density shift. The reported NLL increases and low UR values could therefore be artifacts of the network being unable to satisfy both losses. Please provide a theoretical argument linking the score constraint to path probabilities, or a diagnostic experiment (e.g., probability-flow ODE NLL of Df, or trajectories initialized near Df and shown to be repelled) that rules out the artifact interpretation.
  4. [Sec. 4.1 and evaluation protocol] The evaluation omits error bars and repeated runs for every table. Many of the reported differences are small (e.g., Tab. 5 FID 3.08 vs 3.09; Tab. 6 ACC on Dg 75.5 vs 75.8), so the claimed superiority of MSGM over baselines is not statistically established. Furthermore, the manuscript states that NLL can be 'accurately calculated' for SGMs but does not describe the estimator (e.g., probability-flow ODE, importance sampling, or exact likelihood) or the number of samples used; the toy NLL values in Tab. 1 (e.g., 10.91 for a 2D Gaussian mixture) are also implausibly high for a two-dimensional distribution and need clarification.
minor comments (5)
  1. [Sec. 3.2] The dataset citations are inconsistent: Sec. 3.2 cites CELEBA as [1] and MNIST as [24], while Sec. 4.1 cites MNIST as [1] and CelebA as [24]; please correct the references.
  2. [Sec. 4.5] In the inpainting paragraph, the sentence 'altering the source semantics on Dg' should presumably read 'altering the source semantics on Df', given the reported accuracy decrease on Df.
  3. [Tab. 4] The column header 'Unlearning' in Tab. 4 is not defined among the compared methods, and 'Unseen' appears twice; please fix the header and ensure each baseline is described.
  4. [Eq. (7)] Equation (7) applies the squared norm to a scalar dot product; the notation is redundant and should be replaced by a squared scalar or clarified.
  5. [Sec. 4.6] The ablation of the hyperparameter alpha is reported only for MNIST with Orthogonal-MSGM; a sensitivity analysis on other datasets or for Obtuse-MSGM would strengthen the claim that alpha=0.99 is a generally valid default.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: MSGM's unlearning loss and its evaluation metrics are distinct, and the central claim is benchmarked against external baselines.

full rationale

MSGM's derivation does not reduce to its own inputs. The unlearning objectives in Eqs. (7)-(9) directly penalize the dot product between the learned score and the NSFG conditional score, but the reported evaluations (NLL, UR, FID, CLIP/PSNR/SSIM, downstream accuracy) are separate functionals of the resulting model, measured with external classifiers and standard benchmarks. The claim that 'Unseen by Re-training' leaves the score function essentially unchanged is an empirical observation supported by Fig. 1 and Tab. 1, not an assumption imported from prior work. No load-bearing self-citation appears: the cited baselines and diffusion-model foundations (Song et al., Ho et al., Thudi et al., Gandikota et al., Wu et al.) are external prior work, and the present authors do not cite their own previous papers as justification for the method. The NLL increase on Df is partly expected because the loss manipulates the learned score on noised Df samples, but NLL is not the training target, and the qualitative results, FID, and classifier-based UR provide independent evidence. No specific equation is equivalent by construction to the reported prediction, and no fitted parameter is renamed as a prediction. The paper is self-contained against external benchmarks and baselines, so no circular step is identified.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central method relies on one tuned hyperparameter (α) and on the unproven geometric heuristic that modifying score direction controls generation probability. No new particles or physical entities are introduced.

free parameters (1)
  • alpha = 0.99
    Trade-off hyperparameter in Eq. (9) balancing Lg and Lf; tuned via ablation on MNIST (Sec. 4.6).
assumptions (3)
  • standard math The reverse SDE with an accurate score estimate generates samples from the data distribution.
    Standard result in score-based generative models (Song et al., 2021).
  • standard math The conditional score ∇ log p_{0t}(x(t)|x(0)) is analytically known for the VE/VP SDEs used.
    Required to compute Lf in Eqs. (7)-(8).
  • ad hoc to paper Orthogonalizing or making obtuse the model score relative to the NSFG conditional score suppresses NSFG generation.
    Core heuristic of MSGM; no proof is given.

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Cite this review

Pith. "Pith review of Moderating the Generalization of Score-based Generative Model." pith.science (2026). https://pith.science/paper/SBVW6CYS

@misc{pith2026241207229,
  author       = {Pith},
  title        = {Pith review of: Moderating the Generalization of Score-based Generative Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SBVW6CYS}},
  note         = {Machine review of arXiv:2412.07229}
}
read the original abstract

Score-based Generative Models (SGMs) have demonstrated remarkable generalization abilities, e.g. generating unseen, but natural data. However, the greater the generalization power, the more likely the unintended generalization, and the more dangerous the abuse. Research on moderated generalization in SGMs remains limited. To fill this gap, we first examine the current 'gold standard' in Machine Unlearning (MU), i.e., re-training the model after removing the undesirable training data, and find it does not work in SGMs. Further analysis of score functions reveals that the MU 'gold standard' does not alter the original score function, which explains its ineffectiveness. Based on this insight, we propose the first Moderated Score-based Generative Model (MSGM), which introduces a novel score adjustment strategy that redirects the score function away from undesirable data during the continuous-time stochastic differential equation process. Extensive experimental results demonstrate that MSGM significantly reduces the likelihood of generating undesirable content while preserving high visual quality for normal image generation. Albeit designed for SGMs, MSGM is a general and flexible MU framework that is compatible with diverse diffusion architectures (SGM and DDPM) and training strategies (re-training and fine-tuning), and enables zero-shot transfer of the pre-trained models to downstream tasks, e.g. image inpainting and reconstruction. The code will be shared upon acceptance.

Figures

Figures reproduced from arXiv: 2412.07229 by the authors.

Figure 1
Figure 1. Comparsions of score functions of Standard VE SDE, [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The samples from the mixture Gaussian distribution and the samples generated by the model trained by Standard VE SDE (a), [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Unintended generalization in high-dimensional data via [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Image generation using different unlearning methods for VE SDE on MNIST and VP SDE on CelebA. The top, middle, and [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Visualization of diverse unlearning methods applied [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 8
Figure 8. Figure 8: The comparison of reconstruction results on the CIFAR [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: The visual results of Simultaneously Updating vs. Alter [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.