Feature Likelihood Divergence: Evaluating the Generalization of Generative Models Using Samples

The past few years have seen impressive progress in the development of deep generative models capable of producing high-dimensional, complex, and photo-realistic data. However, current methods for evaluating such models remain incomplete: standard likelihood-based metrics do not always apply and rarely correlate with perceptual fidelity, while sample-based metrics, such as FID, are insensitive to overfitting, i.e., inability to generalize beyond the training set. To address these limitations, we propose a new metric called the Feature Likelihood Divergence (FLD), a parametric sample-based metric that uses density estimation to provide a comprehensive trichotomic evaluation accounting for novelty (i.e., different from the training samples), fidelity, and diversity of generated samples. We empirically demonstrate the ability of FLD to identify overfitting problem cases, even when previously proposed metrics fail. We also extensively evaluate FLD on various image datasets and model classes, demonstrating its ability to match intuitions of previous metrics like FID while offering a more comprehensive evaluation of generative models. Code is available at https://github.com/marcojira/fld.

Paper

References (46)

Scroll for more · 34 remaining

Similar papers

Peer review

Reviewer V3Uo7/10 · confidence 4/52023-07-02

Summary

The paper suggests a sample-based method (termed FLS) for evaluating generative models. Similarly to FID and IS, the method uses a pre-trained network (InceptionV3 or CLIP) for image representation. Unlike FID, the proposed metric is based on a variant of KDE - fitting isotropic Gaussians around each generated sample and choosing variance values that maximize the likelihood of a subset of train samples. The metric is then the test likelihood. The authors claim and demonstrate that FLS is good at measuring the fidelity, novelty and diversity of generated samples and specifically has the advantages of being able to detect overfitting and memorization.

Strengths

Significance: The ability to quantitively assess the quality of image generation models is highly important, especially due to the recent success and impact of "generative AI". There hasn't been much progress in this area in recent years - FID was introduced in 2017 and is still the most commonly used evaluation method and the de-facto standard. Works in this area therefore have high potential impact and should be encouraged. The proposed method seems to have advantages over FID (e.g. the ability to detect memorization and over-fitting). Clarity: The paper is very clearly written and is easy to follow. The motivation is clearly stated and the method is well explained. (I do however have some comments about missing information, in the following sections) The proposed method of using a KDE-like approach rather than some divergence seems to be original and well motivated.

Weaknesses

Missing information: It is stated that FLS uses "Inception-V3 or CLIP" feature space, however it wasn't clearly indicated what feature space was actually used in each experiment (at least, I couldn't find this information). In addition, I would expect to see an analysis of the different behavior of these two representations (pros and cons of each). Additional information that I could not find was the number of samples used for FLS evaluation and how it compares with the number of samples needed for FID. This specifically raised a concern because KDE methods (fitting a Gaussian around each sample) in general require a large number of samples. I would also expect that the ability to detect overfit depends on the number of used samples.

Questions

About the correlation between FLS and Sample Fidelity (4.1). Can the authors explain what causes this correlation and the different behavior than in FID? Is it the embedding network or the different approaches to compare distributions? Have the authors tried evaluating more recent generative models (e.g. Stable Diffusion) on larger datasets (e.g. LAION)? Showing that FLS can scale to these models and dataset can strengthen the significance of the paper. The proposed method seems to be somewhat related to the NDB evaluation method proposed in [1]. [1] E Richardson, Y Weiss, On GANs and GMMs, Advances in neural information processing systems, 2018

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

3 good

Limitations

A discussion about limitations of the proposed method seems to be missing. One example of such possible limitation is the ability of FLS to scale up to modern image-generation models (e.g. trained on the LAION dataset), generating a much larger variability of images (can the KDE-like approach capture this diversity ?) I could not identify a possible negative social impact.

Reviewer HK8L7/10 · confidence 4/52023-07-06

Summary

The work proposes a new metric (FLS) for image generation tasks that is motivated by the observation that current metrics consider the quality and the diversity of the samples, but not their novelty, and therefore are not penalized by memorization of the training set. The proposed method instead encompasses all three aspects in a single evaluation. To compute the score, they extract features from the generated, training, and test images. They then build a mixture of isotropic Gaussians centered around the embeddings of the generated samples. The variances are optimized to maximize the log-likelihood of samples of the training set. FLS is then the likelihood of the test samples. The properties of the metrics are demonstrated by evaluating a number of well-established GAN models.

Strengths

- The paper is well-motivated. While memorization was not much of an issue for generative models so far, some recent study indicates that this might be the case now with the introduction of new powerful generative models. A holistic evaluation including novelty would be a useful tool going forward. - The principles behind FLS are well-grounded in already established methods (FID, Precision/Recall) and the changes are sound and motivated. - FLS is not biased by the number of samples and can therefore be compute on a smaller number of points than FID. - Experiments are extensive, covering many common use-cases including truncation trick, and show promising results. In particular, FLS correlates well with other metrics when memorization is not an issue and the overfitting detection experiments in the main paper and the supplementary are convincing enough.

Weaknesses

A very important aspect is the reliability of FLS w.r.t the number of evaluation samples. As with FID, in practice, people will use the metric in diverse settings and it is important to know when the metric is reliable and when it isn't. The paper touches upon these questions in Fig. 10 but could be more complete. In particular: - Since the models we compare display very little overfitting, Fig 10 only evaluates the robustness of FLS on the Quality and Diversity aspects, not on the Novelty aspect. As novelty evaluation is one central selling point of the metric, information about the reliability of the overfitting detection aspects is necessary. - For the Quality and Diversity aspects, FLS should also be compared to KID, which tackles this same issue of sample size bias. When evaluating with a smaller number of samples, standard deviation should also be provided to better assess the test size that would be needed in practice. Some intervals are depicted in Fig10 but they are barely visible and not commented on at all. FLS might be harder to interpret intuitively than FID. There is a chance that it could lead to misuse or misunderstandings down the road. - In the results presented Fig5, FLS is less linear than FID w.r.t. the % of perturbed data. I would guess this effect is caused by the fact that the variance is adaptive, leading to complex interactions between the samples. This could make the interpretation of the values even less intuitive, as we are more used to linear scales. - In the same figure, until larger percentages of perturbed data, random rotation, elastic transforms, center crops and bicubic resizes all seem to yield the same FLS, while FID assigns different values to different perturbations. As far as I'm concerned, FID results seem more aligned with my intuitions than FLS. Other weaknesses: - FLS might be unsuited to easier tasks. Most well-performing models are nearly indistinguishable by FLS in Table 2 (conditional cifar10). - The computation of FLS has more steps than FID, making it more cumbersome to use. It is also more compute-demanding when scaling.

Questions

My main concerns are, for the sake of practical usage, about the assessment of the minimum number of samples needed: - Can the authors provide a reliability assessment for overfitting detection in few-sample settings? - Can the authors update Fig.10 with KID and standard deviations? - Accordingly, can the authors provide recommendations in terms of the minimal number of samples for reliable assessment? Related to Fig5 and the related discussion in Section 4.1: - the authors mention that “FLS is noticeably less affected”, but it is not that clear since we don't have a scale on which to compare the two metrics. Can the authors explain more explicitly how they derive this observation? As an additional question, one aspect that can be useful in some cases is adversarial perturbation detection. - How do the authors anticipate the metric to behave when faced with adversarially perturbated images? Considering it is supposed to be more robust to noise, it might not be affected by such perturbation. This can be a good or bad thing depending on the task to be evaluated, but useful to know regardless. As a final comment, because the paper is proposing a holistic metric, I believe it might be important for the paper to include, in a separate section, a discussion summarizing good practices and recommendations about when and how to use it.

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Limitations are adequately discussed in the paper and broader impacts in the supplementary.

Reviewer SDnT6/10 · confidence 4/52023-07-06

Summary

The paper proposes an approach for evaluating generate images by fitting a mixture of Gaussians (MoG) to feature embeddings extracted from the generated and real images. For this, images are first mapped to a feature space (e.g. via an Inception or CLIP image encoder) and then map a Gaussian distribution to each image feature with the mean being centered at the specific image feature. The variance of each Gaussian is then optimized via NLL such that the MoG fits the training examples or a subset thereof. The MoG can then be used to evaluate image memorization (any Gaussian with near-zero variance will be a memorized sample) and overfitting (if the MoG assigns higher likelihood to the train set than to an unseen test set), as well as sample fidelity and diversity. The experiments show that the new metric is more robust to small transformations in image space than FID and generally correlates well with FID, precision, and recall.

Strengths

The approach aims to improve upon existing and well-used metrics such as FID and precision+recall. As such, it is easy to calculate, needs minimal human intervention, and scales to large numbers of images. It also aims to improve the evaluation by detecting overfitting/memorization which many current metrics can't detect. Finally, it can provide more detailed insights into models by evaluating the quality of specific classes individually. The approach also seems to be more robust to using smaller sample sizes (e.g., <5K samples), whereas other metrics such as FID need tens ouf thousands of samples.

Weaknesses

While the approach promises some improvements over other metrics the main improvement seems to be being able to detect overfitting and memorization. However, I am not convinced that feature embeddings are the best way to detect memorization. E.g., looking at the memorized results in Fig 8, those results don't look like memorization to me. Were these obtained based on Inception or CLIP embeddings? More detailed insights into the performance of specific classes is also already possible with other metrics, e.g., conditional FID. Aside from that the main other advantage seems to be that the approach is more sample efficient but that is a minor difference since calculating FID and other metrics is usually not the computationally intensive part of model training and evaluation.

Questions

I also wonder about the relationship between this approach and precision+recall. Couldn't precision+recall also be used for detecting memorization and overfitting by applying a similar approach as this one here, applied to the distances already calculated by precision+recall? Would that be simpler? Would the results agree with the results of this metric?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

My main concern is that the most obvious improvement of the new evaluation method, namely easily detecting memorization and overfitting, may not work as expected since it relies on image embeddings from feature extractors that were not trained for this (neither Inception nor CLIP were trained to detect memorization and instead focus more on high-level features). I would not define image in Fig 8 as memorizations. Aside from that, other improvements/differences seem marginal compared to existing metrics such as FID and precision+recall and it's not clear to me what exactly makes the new metric better than, e.g., FID. --- I have adjusted my score to WA based on the author's rebuttal.

Reviewer cRFc7/10 · confidence 4/52023-07-07

Summary

This paper addresses the problem that there are currently no sample-based evaluation metrics accounting for the trichotomy between sample fidelity, diversity, and novelty. Likelihood based metrics are not particularly interpretable and sample quality based metrics do not take into account novelty -- they are easy to cheat just by copying the training data. To address these issues, the paper proposes the feature likelihood score (FLS) -- which assesses sample novelty, overfitting, and memorization.

Strengths

* The paper deals with an important problem and proposes an innovative solution. * The paper provides theoretical guarantees that the proposed FLS score can detect overfitting in Proposition 1. * The shows evaluations on a variety of datasets -- CIFAR10, ImageNet, LSUN and AFHQ and on a variety of models -- StyleGAN-XL, SNGAN, LOGAN, LSGAN etc. * The paper is well written and easy to understand.

Weaknesses

* Can the proposed FLS score be extended to Text to image models such as Stable Diffusion or Latent Diffusion. * The datasets considered such as CIFAR10, ImageNet, LSUN and AFHQ are quite limited in size compared to popular datasets such as LAION. The paper should include an analysis of the effect of dataset size on the ability of FLS to detect generated copies of the training set. * The paper should also include an analysis of the effect of image resolution on the FLS score -- as the image resolution increases will the FLS score be able to detect copies of the training set images? * In Figure 7 (right) why does the FID increase for some models when the % copied samples increases.

Questions

* The paper should motivate in more detail why the CIFAR10, ImageNet, LSUN and AFHQ datasets were choosen as the evaluation platform. * Is the FLS score applicable to text to image models? Can the FLS model detect duplicates in case of text to image models? * Does the FLS show the same behavior on very large datasets such as LAION as on smaller datasets such as CIFAR10 or ImageNet?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The paper does not discuss the limitations of the FLS score in detail. The paper should ideally also failure cases to highlight limitations -- where copied training examples do not degrade the FLS score -- if observed.

Reviewer euCm6/10 · confidence 5/52023-07-13

Summary

Limitation of existing evaluation metrics * Likelihood-based metrics rarely correlated with perceptual fidelity. * Sample-based metrics are insensitive to overfitting. E.g., FID * Copycat (=a model randomly outputs training set) outperforms SOTA generators in $\text{FID}_\text{test}$ Proposed evaluation metric: feature likelihood score (FLS) 1. Map generated / train / test images to an embedding (Inception-v3 or CLIP). 1. Initialize isotropic Gaussians centered at the generated samples. 1. Update the variance of above Gaussians to maximize the likelihood of training samples. 1. Compute the NLL of test samples on the Gaussians. It measures * Novelty = opposite of Memorization * a generated sample is $\delta-$ memorized if NLL of the training set is $\delta-$ lower than the test set on the Gaussian of the generated sample. * Diversity * Empirically shown * Fidelity * Empirically shown FLS is high when * The generated samples have poor quality -> Gaussian centers are far from the test set -> high test NLL * The generated samples do not cover the data manifold -> high test NLL * The generated samples overfit to the training set -> high test NLL

Strengths

* It measures novelty, fidelity, and diversity of generated samples. (not fully explained below) * FLS correlates to sample fidelity (actually, corruption) as FID does. * It is a one-value metric that reflects three aspects. It is easy to rank different models. * The authors provide the benchmark table of SOTA models.

Weaknesses

1. A super-close literature is missing: [rarity score] 1. Some important definitions are missing. E.g., training/test split, L189 data manifold 1. FLS correlates to sample fidelity not as linearly as FID 1. The mechanism how FLS correlates with sample fidelity/diversity is not described (although straightforward). 1. It is a one-value metric that reflects three aspects. It is difficult to compare different aspects with same value. 1. FLSs for different k and C are not provided. 1. Train FLS and test FLS are not defined. minor 1. Figure 5 middle shows FID but caption describes it differently. 1. Figure 5 right shows FLS versus Precision but caption describes it FLS versus Recall.

Questions

1. Why should the SOTA generators be better than the copycat? 1. Could you clarify the difference between definition 3.1 and 3.2 other than the margin $\delta$? 1. How do diversity, fidelity, and memorization affect the metric? Is there a metric affects more than another? To me, Q3 is the most important.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Use cases on non-natural images are not shown (mentioned as future work).

Reviewer HK8L2023-08-10

I thank the authors for the rebuttal and appreciate their consideration of my remarks. My concerns have been convincingly addressed, and I believe the new additions that emerged will be valuable. In particular, I agree with the authors that linearity w.r.t. the percentage of perturbed data is not that important, especially compared to the results in Figure 1 of the rebuttal. Among other things, I also appreciated the recommendations that look reasonable, the updates on KID, and the discussions w.r.t. imperceptible perturbations. From the responses to other reviews, the DINO features experiments in particular would be a very nice addition, providing new insights for generative model evaluation in general beyond this specific method. I will take these elements into account in my final assessment along with the updates from other reviewers before the end of the discussion period. Update: I am raising my rating from WA to Accept

Reviewer euCm2023-08-11

I appreciate the rebuttal. My minor concerns are addressed. One last thing I care the most is usefulness of the proposed metric related to W5 (one metric) and Q3 (impact of aspects to FLS). It is helpful that the rebuttal pdf reports how FLS changes along fidelity, diversity, and memorization. However, I am not sure if I will use FLS instead of FID unless I want a generative model for data augmentation for discriminative model. Different users have different needs. Users do not know which aspect is affecting FLS. As mentioned by the authors in the rebuttal, FLS might be the same for two models: one model produces 90% good images and 10% bad images with 20% memorization, and another model produces 80% good images and 20% bad images with 10% memorization. As the quality of generated images have been saturated recently, I think we need more specific measures for different aspects.

Authorsrebuttal2023-08-12

We thank the reviewer for their prompt response and willingness to engage in discussion. We believe they bring up two very pertinent points. ## Utility of FLS over FID > I am not sure if I will use FLS instead of FID unless I want a generative model for data augmentation for discriminative models. Different users have different needs. We understand the stickiness of FID as a metric and appreciate its utility. In fact, in most scenarios, we show that FLS largely agrees with FID and yields a similar model ranking (Figure 9.). However, we point out multiple failure modes of FID in the paper and show how they are addressed by FLS. - **Heavy bias for smaller samples**: FID displays heavy bias, even up to 50k samples. FLS on the other hand works better with smaller sample sizes which makes it significantly more amenable to evaluating class-conditional generation (where there are often less than 10k samples per class) and for finding problematic classes/issues with conditional alignment. - **Insensitivity to overfitting/memorization**: FID as it is currently computed (comparing with train samples) decreases with memorization and even when compared to test samples, a model copying the training set gets a SOTA FID. - **Sensitivity to imperceptible transformations**: Very slightly altered samples can yield considerably worse FID scores. As shown in Fig.3 of the rebuttal PDF, such transforms cause samples from a SOTA model to be rated as worse by FID than those produced by a 5 year old model. As such, small changes in image processing can have disproportionate impacts on FID. As well as other issues [1, 2]. We believe it is problematic to continue using a metric with known issues, especially as these issues are becoming more common. As such, we believe that FLS should be favored in most cases and especially when working with smaller datasets. Moreover, note that in our latest experiment (Table 1 of the rebuttal PDF) we observe that FLS with DINOv2 showcases a trend of the superiority of diffusion models in comparison to SOTA GANs (such as StyleGANXL) which was not clear with FID. ## Multi-faceted evaluation > Different users have different needs. Users do not know which aspect is affecting FLS[...] I think we need more specific measures for different aspects. We completely agree that specific metrics (such as precision, recall, rarity score, etc.) are very valuable and should be used to evaluate specific aspects of the best-performing models, but such a diagnosis is complementary to benchmarking and ranking using a single holistic metric. In fact, the use of a single metrics by practitioners is undeniable: - **Generative modeling for image data:** FID is by far the most used metric. - **Machine translation:** Practitioners have been reporting the F-score [3, 4] which trades off precision and recall, or the BLEU score (a precision oriented metric). - **Supervised classification:** Practitioners often use standard accuracy to evaluate their models even though some datasets have been saturated. Even for unbalanced dataset practitioners often report F1 score [5]. This can be explained by: - Comparing two models with respect to several metrics is more challenging since they may be on the Pareto front ($\mathcal{R}^2$ (fidelity, diversity) or $\mathcal{R}^3$ (fidelity, diversity, novelty) are not totally ordered). - When considering metrics such as precision and recall a model could over-optimize one which corresponds to a pathological behavior while still being on the Pareto front. #### Flexibility of our Method We would like to point out the flexibility of the feature likelihood methodology. We believe this form of density estimation allows for measuring various aspects of generative model evaluation not possible with FID: - **Overfitting evaluation:** The % of overfit Gaussians and the generalization gap allow specifically for evaluating the overfitting behavior quantitatively. If the issue affecting FLS is overfitting, it can be picked up by these methods. - Ranking of memorized samples provides a way to qualitatively evaluate memorization by the model - **Fidelity evaluation**: If we estimate the density of the data distribution by using Gaussians centered at the test set, we can then use this to evaluate the likelihood of the generated samples (and thus find high-quality samples, such as in Appendix A.3). - The likelihood of the whole dataset could be a quantitative measure of fidelity. [1] Kynkäänniemi, Tuomas, et al. "The Role of ImageNet Classes in Fr\'echet Inception Distance."(2022). [2] Parmar, Gaurav, Richard Zhang, and Jun-Yan Zhu. "On aliased resizing and surprising subtleties in gan evaluation." 2022. [3] Van Rijsbergen, Cornelis Joost. "Foundation of evaluation." 1974. [4] Derczynski, Leon. "Complementarity, F-score, and NLP Evaluation." 2016. [5]Wang, Xudong, et al. "Long-tailed recognition by routing diverse distribution-aware experts." 2020.

Reviewer euCm2023-08-15

I appreciate thorough discussion. My concerns are resolved and I am changing my score from BA to WA. Adding the discussion to the revised version would make the paper stronger.

Reviewer V3Uo2023-08-11

I thank the authors for the thorough rebuttal. Specifically, the fact that FLS does not require an especially large number of samples and is an unbiased estimator is reassuring. I still think handling the new large generative models and datasets would have increased the impact of the method, but I agree with the authors that this can be future work.

Reviewer SDnT2023-08-15

Thanks

I thank the authors for their extensive response. Using Dino features instead of Inception features does indeed seem to work much better, especially for very close neighbors. The response regarding precision+recall addressed my thoughts and I also especially like Fig 1 of the rebuttal and its implications. I have adjusted my score to WA.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

© 2026 NYSGPT2525 LLC