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REVIEW 4 major objections 5 minor 64 references

Diverse Rare Sample Generation with Pretrained GANs

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

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Pith's one-line read A pretrained GAN can be steered to generate rare, diverse images by optimizing latent vectors against a learned density estimate, with no retraining or fine-tuning of the generator.

desk verdict Useful, practical rare-sample generation method with real novelty, but the missing no-Lrare ablation leaves the normalizing-flow mechanism under-supported. read the letter →

arxiv 2412.19543 v2 pith:B3V4B6GG submitted 2024-12-27 cs.CV

Subeen Lee , Jiyeon Han , Soyeon Kim , Jaesik Choi This is my paper · ORCID
classification cs.CV
keywords raresamplegenerationpretrainedGANslatentspaceoptimizationnormalizingflowsdensityestimationmulti-objectivek-NNrarityscorediversitycontrol
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

Generative models produce realistic images but rarely the unusual cases that sit in low-density regions of the data manifold, and methods that improve fidelity often shrink diversity. This paper claims that a pretrained GAN can be pushed to generate rare images — faces with hats, non-brown hair, extreme ages, non-frontal poses, uncommon breeds — by running gradient descent on its latent vectors with a multi-objective loss, without retraining or fine-tuning the generator. The rarity signal is a normalizing flow that estimates the log-density of real images in a deep feature space; minimizing $\log p(x)$ drives generated samples toward low-density regions. A repulsion term between simultaneously optimized latents enforces diversity, a boundary term keeps each result similar to a chosen reference image, and a manifold constraint keeps outputs realistic. If correct, the method turns any pretrained GAN into a controllable supplier of rare, varied images, which matters for building synthetic datasets that cover underrepresented cases.

What carries the argument

The load-bearing object is the multi-objective latent objective of Eq. (2), made differentiable by replacing the k-NN rarity score with a normalizing-flow density estimate. A Glow-style flow — a stack of invertible layers that turns a simple base distribution into a complex one while giving exact per-sample log-likelihoods — is trained on VGG16-fc2 features of real images, so $\log p(x)$ serves as a smooth stand-in for rarity; the paper reports Pearson correlations of 0.928 for real and 0.815 for fake samples between the two measures. The similarity term $(\max\{d(x,x^*)-d^*,0\})^2$ with boundary $d^*$ taken from the fake k-NN manifold keeps optimized images near the reference, the diversity term $-\sum_{j \neq i} d(x_i,x_j)^2$ pushes multi-start solutions apart, and feasibility is enforced by requiring each optimized feature to lie inside the real k-NN manifold $\Phi_{\mathrm{real}}$. Multi-start initializes each run at $z^* + \epsilon$ with $\epsilon \sim \mathcal{N}(0,\sigma^2 I)$, and Adam with a step scheduler performs the optimization.

What would settle it

On the FFHQ–StyleGAN2 outputs (10,000 optimized samples), compute the Pearson correlation between flow log-likelihood and k-NN rarity score restricted to the low-likelihood tail, say the bottom 10% by $\log p$; if the correlation collapses toward zero or reverses sign inside that tail, or if the highest-rarity samples are predominantly the kind of manifold artifacts the authors concede are 'inevitable' in the appendix, then the differentiable surrogate is not driving the metric it claims to optimize. A second decisive check: replace the flow with a smooth surrogate trained directly on k-NN rarity values; if it matches or beats the flow-driven results, the flow is incidental rather than load-bearing.

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Extended reading notes

Core claim

The paper's central claim is that generating rare images from a pretrained GAN reduces to a constrained, multi-objective optimization over latent vectors. Starting from a reference image $x^* = f(G(z^*))$ in a deep feature space, the method solves $$\min_{z_i}\; \log p(x_i) + \lambda_1 (\max\{d(x_i,x^*)-d^*,0\})^2 - \lambda_2 \sum_{j \neq i} d(x_i,x_j)^2\quad \text{subject to } x_i \in \Phi_{\mathrm{real}},\; d(x_i,x^*) \leq d^*,$$ where $p$ is the normalizing-flow density of real images in that feature space, $\Phi_{\mathrm{real}}$ is the union of k-nearest-neighbor balls around real samples, and $d^*$ is a penalizing boundary derived from the fake k-NN manifold. Minimizing $\log p(x_i)$ pushes samples into low-density regions, the similarity penalty reins them back toward the reference, and the pairwise repulsion spreads distinct latents apart so that multi-start optimization from $z^* + \epsilon$ converges to visually different rare images rather than the same local optimum. Across FFHQ, AFHQ, and MetFaces at 1024×1024 resolution, this raises the k-NN rarity score and pairwise LPIPS diversity relative to baseline sampling while holding precision at 0.76–0.92, and it increases the measured prevalence of rare facial, breed, and painting-style attributes.

Load-bearing premise

The method assumes the normalizing flow's density estimate, trained on ordinary real images, stays accurate in exactly the low-density regions the optimizer seeks out, so that minimizing $\log p(x)$ reliably raises the k-NN rarity score used for evaluation — the reported correlation of 0.815 on fake samples is evidence for the surrogate but not a guarantee that the two measures agree where rarity matters most.

Editorial extensions

If this is right

  • Rarity, diversity, and similarity to the reference become user-set knobs: $\lambda_1$ controls how close results stay to the reference, $\lambda_2$ controls how far apart the rare samples spread, and the noise scale $\sigma$ and boundary parameter $k'$ set how far the optimizer roams.
  • No retraining or fine-tuning of the generator is needed; the only per-dataset cost is training the density estimator, reported as under 30 minutes on a single GPU, after which any reference latent can be turned into rare variants.
  • Across FFHQ, AFHQ Cat, AFHQ Dog, and MetFaces at 1024×1024, the method raises the rarity score and pairwise LPIPS diversity over baseline sampling while keeping precision between 0.76 and 0.92, compared with 0.38–0.39 for the Polarity baseline, which generates many out-of-manifold artifacts.
  • Measured rare-attribute prevalence increases on all datasets — hats, eyeglasses, baldness, non-brown hair, extreme age, non-white race, and non-frontal poses among faces; minor cat and dog classes; and non-Western painting styles — so synthetic data can be deliberately enriched with underrepresented cases.
  • A single reference yields several visually distinct rare images rather than one, because the diversity term keeps the multi-start runs from collapsing into the same local optimum.

Reading between the lines

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

  • The 0.815 correlation between flow likelihood and k-NN rarity on fake samples is the bridge the whole method crosses; a direct check of whether that correlation survives inside the low-likelihood tail the optimizer targets would tell whether the surrogate is truly driving the evaluated metric.
  • Nothing in the objective is GAN-specific, so the recipe — replace a non-differentiable rarity or fidelity metric with a trained differentiable density model on deep features — should transfer to diffusion models, where low-density guidance has so far relied on class-conditional Gaussian assumptions.
  • Because diversity is a pure geometric repulsion in feature space, the number of distinct rare attributes reachable per reference is bounded by the generator's latent geometry; attribute diversity should saturate as $\lambda_2$ grows while rarity eventually falls, a pattern already visible in the paper's parameter sweep.
  • The FID cost on FFHQ (4.17 to 7.38) is structural rather than a defect: any method that deliberately moves mass to low-density regions worsens distribution-level fidelity metrics, so applications should judge rarity-augmented data by task-level outcomes such as classifier accuracy on rare classes rather than by FID alone.
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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 proposes DivRareGen, a training-free method for generating diverse rare samples from a pretrained GAN. It optimizes latent codes with a multi-objective loss that combines a normalizing-flow log-likelihood term as a differentiable rarity proxy, a one-sided similarity penalty anchored at a reference image, and a pairwise diversity term, subject to constraints that keep samples inside the real-data k-NN manifold and within a similarity boundary. The method is evaluated on FFHQ, AFHQ, and MetFaces with StyleGAN2 variants, reporting improved rarity scores, diversity, and increased prevalence of rare semantic attributes, alongside higher FID/KID values.

Significance. If the central mechanism is verified, the method would be a practically valuable, retraining-free way to explore low-density regions of a pretrained GAN with user-controllable rarity, diversity, and reference similarity. The paper contributes a clear optimization formulation, public code, extensive appendices, and a useful correlation analysis between NF-estimated density and k-NN-based rarity. However, the ablation study does not isolate the contribution of the NF rarity term, and the evaluation pipeline has selection issues (hyperparameters chosen on the evaluation metrics, rarity scores computed after excluding undefined cases). These issues currently leave the paper's main claim unproven, so the result is promising but requires substantial verification.

major comments (4)
  1. [§4.3, Table 7] The ablation in Table 7 does not isolate the normalizing-flow rarity term. With Lrare alone the rarity score is 18.99, essentially equal to the baseline of 18.88 reported in Table 1, and the improvement appears only after adding Lsim (21.11) and Ldiv (21.28). Since the paper never evaluates the full objective without Lrare, the evidence is consistent with the NF term contributing nothing beyond the similarity boundary and diversity constraint; the method could reduce to constrained multi-start diversity optimization. Please add the Lsim + Ldiv configuration (without Lrare) and report both RS and LPIPS, so the role of the NF density estimator is actually tested.
  2. [§4.1 and Appendix C] The hyperparameters λ1, λ2, σ, and k′ are selected using the same rarity score and LPIPS metrics on the evaluation setup. Appendix C, Tables 9–11, reports RS/LPIPS for different values on the FFHQ-StyleGAN2 setting that later produces the headline results in Table 1, which is tuning on the test distribution and can inflate the reported improvements. Please provide a validation-based selection procedure or a sensitivity analysis that does not use the evaluation metrics for model choice, and report confidence intervals for RS, precision, recall, and FID/KID, not only for LPIPS.
  3. [§4.1, Table 1] The text in Section 4.1 states that 'The FID score decreases,' but Table 1 shows FID increasing from 4.17 to 7.38 (higher is worse), and Table 4 shows KID increasing for all three datasets. This misstates the fidelity trade-off. Please correct the wording and explicitly discuss the fidelity cost, especially because the introduction and conclusion emphasize avoiding low-quality samples and the method's precision score is high, which creates an apparent tension with the large FID/KID degradation.
  4. [§4.1 and Appendix C] Rarity-score computations in the paper exclude samples with undefined rarity scores: Appendix C states 'mean rarity score except for the undefined rarity cases,' and the method produces 11–14% out-of-manifold samples (Tables 9 and 10). If the headline RS in Table 1 is also computed on the in-manifold subset only, the observed improvement may partly reflect this filtering rather than the optimization itself. Please report the out-of-manifold percentage for the main experiments and state unambiguously how undefined rarity scores are treated in every reported RS value.
minor comments (5)
  1. [§3.2, Eqs. (1)–(2)] The Lsim term is zero whenever d(x, x*) ≤ d*, so it only penalizes violations of the similarity boundary and does not actively attract the solution toward the reference. Please clarify whether the constraint is enforced by projection or by penalty, and why both the constraint and the Lsim term are needed.
  2. [Figure 2] The typeset objective in Figure 2 is missing operators between terms (the expression reads as a concatenation of −λ2 sum, +λ1 max, and log p(xi)). Please fix the equation formatting.
  3. [§4.3, Table 7] The full-objective RS in Table 7 is 21.28 for 100 initial latent vectors, while the corresponding setting in Table 1 reports RS 23.50 for 1,000 initial latent vectors. Please explain this difference (sample size, parameter variation, or random seed) so readers can reconcile the two tables.
  4. [Table 3] The caption of Table 3 says 'Sorted in descending order of FFHQ(%),' but the rows are listed in ascending order of FFHQ(%) (0.12, 0.39, 0.88, ...). Please correct the caption or the ordering.
  5. [§4.4] The correlation analysis in Figure 8 excludes samples with undefined rarity scores; please state this explicitly in the main text rather than only in the figure context, since it affects the interpretation of the reported 0.815 correlation for fake samples.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NF rarity objective is an independent differentiable proxy, the rarity-score metric is an external evaluation criterion, and the derivation is self-contained.

full rationale

I walked the derivation chain from Eq. (1)-(2) through the ablation and evaluation sections and found no step where a claimed prediction reduces by construction to its inputs. The rarity objective Lrare(x)=log p(x) is the log-likelihood of a Glow normalizing flow trained on real VGG16 feature vectors; the evaluation metric is the k-NN rarity score of Han et al. (2023). These are different functions, and the paper explicitly measures their empirical correlation (Pearson 0.928 real / 0.815 fake) rather than assuming identity. The self-citation to Han et al. is used as an external evaluation metric, not as a premise of the optimization, so it is not load-bearing in the derivation. The similarity and diversity terms are standard regularizers, and the real k-NN manifold constraint is borrowed from independent metric literature. Parameter choices in Appendix C are tuned on a subset of the same dataset, which is a methodological weakness but not a circularity: the reported test set uses 1,000 initial vectors while tuning uses 100, and the objective is an optimization over latent codes, not a fitted predictor of the reported metric. The strongest internal concern is Table 7: Lrare alone yields RS 18.99 versus baseline 18.88, so the NF term alone does not drive the rarity improvement, and the paper does not ablate the full objective without Lrare. This is an attribution/ablation gap about which term contributes, not a circularity: it does not make the final rare-sample generation equal to the NF density by definition. The reliance on NF density estimates in unexplored low-density regions is a correctness risk, not a circular step. Overall, the paper is not circular.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The method introduces no new physical entities. It relies on a trained normalizing flow and a set of hand-chosen hyperparameters. The key assumptions are the reliability of the NF as a rarity surrogate and the validity of the k-NN manifold constraints.

free parameters (4)
  • lambda_1 (similarity weight) = 30.0 (FFHQ), 200.0 (AFHQ, MetFaces)
    Controls how strongly samples are penalized for exceeding the similarity boundary; chosen by sensitivity analysis in Appendix C.
  • lambda_2 (diversity weight) = 0.002 (FFHQ), 0.02 (AFHQ, MetFaces)
    Controls pairwise diversity in the multi-objective loss; chosen by sensitivity analysis in Appendix C.
  • sigma (noise scale for multi-start) = 0.1 (FFHQ), 0.01 (AFHQ, MetFaces)
    Determines the initial perturbation of latent vectors; chosen so fewer than 30% of initial perturbed latents go outside the real k-NN manifold.
  • k' (nearest-neighbor order for penalizing boundary) = 100
    Sets the radius of the similarity boundary d*; chosen by sensitivity analysis in Appendix C.
assumptions (5)
  • domain assumption The normalizing flow density in VGG16 feature space is a valid proxy for rarity as defined by k-NN distance.
    Eq (1) uses log p(x) as the rarity objective; if the NF is miscalibrated in low-density regions, the optimization could produce out-of-distribution samples. Section 3.2.
  • domain assumption The real k-NN manifold (k=3) accurately distinguishes in-distribution from out-of-distribution feature vectors.
    Used as a hard constraint in Eq (1)-(2); the paper acknowledges overestimated manifold regions in Appendix D.2.
  • domain assumption The GAN's latent space is continuous enough for gradient-based optimization to find diverse rare points while staying in the manifold.
    Implicit in the use of Adam on latent vectors; the method assumes that rare regions are reachable by local search.
  • domain assumption VGG16 feature Euclidean distance is a valid perceptual similarity metric.
    Used for Lsim and Ldiv, cited from Zhang et al. 2018.
  • ad hoc to paper The fake k-NN manifold estimated from 10,000 GAN samples is representative for defining d*.
    Used to set the similarity boundary in Eq (1); depends on the specific set of generated samples.

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Cite this review

Pith. "Pith review of Diverse Rare Sample Generation with Pretrained GANs." pith.science (2026). https://pith.science/paper/B3V4B6GG

@misc{pith2026241219543,
  author       = {Pith},
  title        = {Pith review of: Diverse Rare Sample Generation with Pretrained GANs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B3V4B6GG}},
  note         = {Machine review of arXiv:2412.19543}
}
read the original abstract

Deep generative models are proficient in generating realistic data but struggle with producing rare samples in low density regions due to their scarcity of training datasets and the mode collapse problem. While recent methods aim to improve the fidelity of generated samples, they often reduce diversity and coverage by ignoring rare and novel samples. This study proposes a novel approach for generating diverse rare samples from high-resolution image datasets with pretrained GANs. Our method employs gradient-based optimization of latent vectors within a multi-objective framework and utilizes normalizing flows for density estimation on the feature space. This enables the generation of diverse rare images, with controllable parameters for rarity, diversity, and similarity to a reference image. We demonstrate the effectiveness of our approach both qualitatively and quantitatively across various datasets and GANs without retraining or fine-tuning the pretrained GANs.

Figures

Figures reproduced from arXiv: 2412.19543 by the authors.

Figure 1
Figure 1. Examples of rare samples generated by our method. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Schematic diagram for the objective function of our method. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Examples of rare samples generated by our method [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (15 more)
Figure 5
Figure 5. Figure 5: Examples of diverse rare samples generated by our [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 7
Figure 7. Figure 7: Examples of rare samples generated by our method [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 6
Figure 6. Figure 6: Examples of high- and low-likelihood real samples [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: Correlation plot for the k-NND / rarity score and negative log-likelihood estimated by the normalizing flow. samples inside the boundary. Finally, incorporating the Ldiv completes the full objective. The results in [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 10
Figure 10. Figure 10: Examples of diverse rare samples generated [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: Examples of diverse rare samples generated by [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 12
Figure 12. Figure 12: Additional rare samples generated by our method using FFHQ-StyleGAN2. In each row, the first and third columns [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: Comparative qualitative results: FFHQ-StyleGAN2 with a truncation value of [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 14
Figure 14. Figure 14: Examples of diverse rare samples generated by our method using AFHQ and MetFaces with StyleGAN2-ADA. [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: With replacement, certain out-of-manifold samples [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: Additional rare samples generated by our method using AFHQ and MetFaces with StyleGAN2-ADA. In each row, [PITH_FULL_IMAGE:figures/full_fig_p018_16.png]
Figure 17
Figure 17. Figure 17: High-likelihood references (top 100) and their optimized rare images generated by our method. Top: FFHQ [PITH_FULL_IMAGE:figures/full_fig_p019_17.png]
Figure 18
Figure 18. Figure 18: High-likelihood references (top 100) and their optimized rare images generated by our method. Top: AFHQ Cat [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]
Figure 19
Figure 19. Figure 19: Examples of the optimization paths with a real [PITH_FULL_IMAGE:figures/full_fig_p021_19.png]
Figure 20
Figure 20. Figure 20: Qualitative results of Polarity sampling with [PITH_FULL_IMAGE:figures/full_fig_p022_20.png]

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

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