Real-World Benchmarks Make Membership Inference Attacks Fail on Diffusion Models

## Abstract

Abstract Membership inference attacks (MIAs) on diffusion models have emerged as potential evidence of unauthorized data usage in training pre-trained diffusion models. These attacks aim to detect the presence of specific images in training datasets of diffusion models. Our study delves into the evaluation of state-of-the-art MIAs on diffusion models and reveals critical flaws and overly optimistic performance estimates in existing MIA evaluation. We introduce CopyMark, a more realistic MIA benchmark that distinguishes itself through the support for pre-trained diffusion models, unbiased datasets, and fair evaluation pipelines. Through extensive experiments, we demonstrate that the effectiveness of current MIA methods significantly degrades under these more practical conditions. Based on our results, we alert that MIA, in its current state, is not a reliable approach for identifying unauthorized data usage in pre-trained diffusion models. To the best of our knowledge, we are the first to discover the performance overestimation of MIAs on diffusion models and present a unified benchmark for more realistic evaluation. Our code is available on GitHub: https://github.com/caradryanl/CopyMark .

## 1 Introduction and Related Works

Diffusion models (Sohl-Dickstein et al., ; Song & Ermon, ; Ho et al., ; Song et al., ) have revolutionized the field of image synthesis. A notable advantage of these models is their ability to train stably on vast web-sourced datasets containing billions of images (Schuhmann et al., ; ). This capability has paved the way for large-scale pre-trained models in image synthesis (Rombach et al., ; Podell et al., ; Chen et al., ; Esser et al., ). However, these pre-trained models have raised concerns regarding unauthorized data usage (Samuelson, ; Sag, ), as their training datasets often include numerous copyrighted images without proper authorization.
In response, copyright owners have initiated a series of lawsuits against producers of pre-trained diffusion models (Andersen, ; Zhang, ). Within this context, membership inference attacks (MIAs) on diffusion models (Duan et al., ; Kong et al., ; Fu et al., ; Wu et al., ; Fu et al., ) have emerged. MIAs aim to separate members (data used for training) and non-members (data not used for training). Their results help determine whether specific images were included in the training dataset of diffusion models, thus being considered as potential evidence of unauthorized data usage in AI copyright lawsuits related to diffusion models.

However, recent research suggests that MIAs on Large Language Models (LLMs) may perform successfully because they are evaluated under defective setups with distribution shift (Das et al., ; Maini et al., ). Their performance is confounded by evaluating on non-members belonging to a different distribution from the members (Maini et al., ). This finding raises concern on the true effectiveness of MIAs, including those on diffusion models.

Inspired by the above idea, we investigate the current evaluation of MIAs on diffusion models. Unfortunately, we find that there are similar defects in the evaluation of MIAs on diffusion models. Specifically, the evaluation is based on 1) over-trained models (Duan et al., ; Kong et al., ; Fu et al., ; Pang et al., ) and 2) member datasets and non-member datasets with distribution shifts (Duan et al., ; Kong et al., ). Both setups make the task of MIA easier than the real-world scenario, with pre-trained diffusion models and unshifted members and non-members. This defective evaluation leaves unknown the true performance of MIAs on diffusion models.

To fill the blank of real-world evaluation, we build CopyMark, the first unified benchmark for membership inference attacks on diffusion models. CopyMark gathers 1) all pre-trained diffusion models (Rombach et al., ; Gokaslan et al., ; YEH et al., ) 2) with accessible unshifted non-member datasets (Dubiński et al., ; Gokaslan et al., ; YEH et al., ). We implement state-of-the-art MIA methods on these diffusion models and datasets. To refine the current evaluation pipeline, we introduce extra test datasets in addition to the original validation datasets (datasets where we find the optimal threshold to separate members and non-members) and use these test datasets for blind test of MIAs. Through extensive experiments, we show that MIA methods on diffusion models suffer significantly bad performances on our realistic benchmarks. Our result alerts the fact that current MIAs on diffusion models only appear successful on unrealistic evaluation setups and cannot perform well in real-world scenarios. Our contributions can be summarized as follows:

- •
We reveal two fatal defects in current evaluation of MIAs on diffusion models: over-training and dataset shifts (Section 3).
- •
We design and implement CopyMark, a novel benchmark to evaluate MIAs on diffusion models in real-world scenarios. To the best of our knowledge, this is the first unified benchmark for MIAs on diffusion models (Section 4).
- •
We are the first to alert that the performance of MIAs on diffusion models has been overestimated through extensive experiments (Section 5). This is significant both theoretically for future research in this area and empirically for people involving in the AI copyright lawsuits who expect MIAs as evidence .

## 2 Background

### 2.1 Diffusion models

Diffusion models (Sohl-Dickstein et al., ; Song & Ermon, ; Ho et al., ; Song et al., ; Dhariwal & Nichol, ) achieve state-of-the-art performance in generative modeling for image synthesis. Diffusion models are latent variable models in the form of $p_{\theta}(x_{0:T})$ with latent variables $x_{1:T}$ sharing the same shape with data $x_{0}\sim q(x_{0})$ (Ho et al., ; Song et al., ). $p_{\theta}(x_{0:T})$ is denoted by reverse process since it samples $x_{t-1}$ by progressively reversing timestep $t$ with $p_{\theta}(x_{t-1}|x_{t})$.

$$ $\displaystyle p_{\theta}(\bm{x}_{0:T})=p(\bm{x}_{T})\prod_{t\geq 1}p_{\theta}( \bm{x}_{t-1}|\bm{x}_{t}),p_{\theta}(\bm{x}_{t-1}|\bm{x}_{t}):=\mathcal{N}(\bm{ x}_{t-1};\mu_{\theta}(\bm{x}_{t},t),\Sigma_{\theta}(\bm{x}_{t},t))$ (1) $$

with $p(x_{T})$ as the prior and set as standard Gaussian. Diffusion models are distinguished by its posterior $q(x_{1:T}|x_{0})$ which is a Markov process that progressively adds gaussian noise to the data, termed by the forward process (Ho et al., ).

$$ $\displaystyle q(\bm{x}_{1:T}|\bm{x}_{0})=\prod_{t\geq 1}q(\bm{x}_{t}|\bm{x}_{t -1}),q(\bm{x}_{t}|\bm{x}_{t-1}):=\mathcal{N}(\bm{x}_{t};\sqrt{1-\beta_{t}}\bm{ x}_{t-1},\beta_{t}\bm{I})$ (2) $$

The model is trained by matching the reverse step $p_{\theta}(\bm{x}_{t-1}|\bm{x}_{t})$ with the forward step $q(\bm{x}_{t-1}|\bm{x}_{t},\bm{x}_{0})$ conditioned on data $\bm{x}_{0}$, where the model learns to sample $x_{0}$ from the prior $p(x_{T})$ by progressively sampling $x_{t-1}$ from $x_{t}$ with $p_{\theta}(x_{t-1}|x_{t})$.

Diffusion models are scalable for pre-training over large-scale text-image data (Rombach et al., ; Podell et al., ; Chen et al., ; Luo et al., ; Esser et al., ). However, pre-trained diffusion models may include copyright images in the training dataset without authorization (Andersen, ; Zhang, ). This unauthorized data usage now raises critical ethics issues.

In this paper, we focus on one family of diffusion models, Latent Diffusion Models (LDMs) (Rombach et al., ). LDMs are the base architecture of state-of-the-art pre-trained diffusion models (Rombach et al., ; Podell et al., ; Chen et al., ; Luo et al., ; Esser et al., ). These models are the origin of the above unauthorized data usage. To investigate whether MIAs on diffusion models are effective tools in detecting unauthorized data usage, we evaluate them on these LDM-based pre-trained diffusion models.

### 2.2 Membership inference attacks on diffusion models

Membership Inferences Attacks (MIAs) (Shokri et al., ; Hayes et al., ; Chen et al., ; Carlini et al., ) determine whether a datapoint is part of the training dataset of certain diffusion models. We give the formal problem statement of MIAs as follows:

Membership Inference Attacks Given the training dataset $\mathcal{D}_{member}$ (members) of a model $\theta$ and a hold-out dataset $\mathcal{D}_{non}$ (non-member), membership inference attacks aim at designing a function $f(x,\theta)$, that $f(x,\theta)=1$ for $x\in\mathcal{D}_{member}$ and $f(x,\theta)=0$ for $x\in\mathcal{D}_{non}$.

Currently, they are two types of MIA methods on diffusion models:

- •
Loss-based MIAs (Duan et al., ; Fu et al., ; Kong et al., ): Loss-based MIAs are built on the general hypothesis that the training loss of members is smaller than that of non-members. They therefore calculate a function $R(x,\theta)\in\mathbb{R}$ for data point $x$ based on the training loss of diffusion models and find an optimal threshold $\tau$ to discriminate $R(x,\theta)$ of members and non-members.
$\displaystyle f(x,\theta):=\mathbbm{1}[R(x,\theta)<\tau]$
(3)
- •
Classifier-based MIAs (Pang et al., ): Classifier-based MIAs believe that members and non-members have different features $g_{\theta}(x)$ in diffusion models. The features could be gradients and neural representations. These features can be used to train a neural network $F$ to classify members and non-members.
$\displaystyle f(x,\theta):=F(g_{\theta}(x))$
(4)

Membership inference attacks of diffusion models are evaluated by two metrics: true positive rate at a low false positive rate (Carlini et al., ) and AUC. Here, true positive rate (TPR) means the percentage of predicting members as members correctly, while false positive rate (FPR) means the percentage of predicting non-members as members falsely. We are interested in this TPR at $X\%$ FPR because we only care about whether some members could be identified without errors in practice. Take detecting unauthorized data usage as an example. With only one copyright image is determined as the member, we can then prove the existence of unauthorized data usage. We also include AUC as our metric, which is a classical measurement on the discrimination of MIA methods. In practice, we calculate TPRs and FPRs on the dataset. Then, we search for the optimal threshold and calculate AUC on the same dataset.

Notably, the evaluation of MIAs need to follow the MI security game protocol (Carlini et al., ; Hu & Pang, ), that the member $\mathcal{D}_{member}$ and the non-member $\mathcal{D}_{non}$ should come from the same data distribution. This is because we do not know the distribution of members and non-members in real-world scenarios of MIAs, for example, detecting unauthorized data usage in pre-trained diffusion models. We then need to assume the worst case when the member and the non-member $\mathcal{D}_{non}$ come from the same data distribution so that we cannot simply distinguish them without the help of model $\theta$. However, we will show in the rest of this paper that this protocol is not well followed in existing MIAs on diffusion models.

## 3 Evaluation of MIAs on Diffusion Models Are Defective

**Table 1: Reviewing previous defective evaluation setups of MIAs on diffusion models. These setups suffer either over-training or dataset shifts.**
| Model | DDPM | DDPM | DDPM | DDPM | DDPM | LDM | LDM | LDM | SD1.5 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Dataset | CIFAR-10 | CIFAR-100 | ImageNet | CelebA | COCO | COCO | Pokemon | CelebA | LAION |
| SecMI | ✓ | ✓ | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ | ✓ |
| PIA | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ |
| PFAMI | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ |
| GSA | ✓ | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ |
| Over-training | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |
| Shifted Datasets | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ |

In this section, we reveal the fundamental defect within current evaluation of MIAs on diffusion models. We start from explaining two choices in the evaluation setup of MIAs:

- •
over-training v.s. pre-training: Over-training refers to overly training a model on a small training dataset, e.g. 30 epochs on CIFAR10. According to Song & Ermon (), over-training will improve the generation performance. Hence, it is considered as a default setup when training small diffusion models. Pre-training, in contrast, means training a model on a very large dataset. Pre-training only involves 1 or 2 training epochs.
- •
shifted datasets v.s. unshifted datasets: Dataset shift means that the member dataset and the non-member dataset do no come from the same data distribution. On the contrary, unshifted member and non-member datasets refer to the condition that the member dataset and the non-member dataset come from the same data distribution.

Over-training and shifted datasets are the unrealistic choice. Specifically,

- •
over-training easily gives rise to over-fitting, since the model is trained for hundreds of steps on each data point from a limited dataset. This over-fitting markably lowers the training loss of members and even causes memorization (Gu et al., ), making it easier to distinguish members from non-members based on training losses. However, recent progress in pre-training diffusion models shows the potential to train photorealistic diffusion models for only 1 epoch on large-scale text-image datasets (Rombach et al., ; Gokaslan et al., ), which does not make the training loss of members much lower than that of non-members (Wen et al., ). Since these pre-trained models are the real-world interests of MIAs on diffusion models, evaluting MIAs on over-trained diffusion models are unrealistic.
- •
dataset shift makes it possible to distinguish members from non-members without accessing the model. Hence, MIA methods succeeding on shifted datasets are probably dataset classifiers (Liu & He, ) that only captures the difference in image semantics, rather than real membership inference attacks. Such dataset classifiers will fail on correctly discriminating members and non-members that come from the same data distribution.

Table 1 examines the evaluation setup of MIAs on diffusion models from the perspective of over-training and shifted datasets and details some commonly used setups. Unfortunately, we find that there are either over-training or shifted datasets or both in these setups. For example, DDPM + CIFAR-10 (member) & CIFAR-10 (non-member) (Duan et al., ; Fu et al., ; Pang et al., ), DDPM + ImageNet (member) & ImageNet (non-member) (Duan et al., ; Fu et al., ; Kong et al., ; Pang et al., ), and LDM + CelebA (member) & FFHQ (non-member) (Fu et al., ) over-train diffusion models for at least 300 iterations on each of the data point. On the other hand, although SD1.5 + LAION (member) & MS-COCO (non-member) (Duan et al., ; Kong et al., ) exploits a pre-trained diffusion model (Rombach et al., ), it picks non-members from MSCOCO, whose distribution is markably different from that of LAION. With over-training and dataset shift, it is unknown whether the success of MIA methods depends on the over-fitting or a non-member dataset whose distribution differs from that of the member dataset. This is a fatal defect of current evaluation of MIAs on diffusion models.

## 4 CopyMark: Real-World Benchmark for Diffusion MIAs

To overcome the defect in previous evaluation and investigate the real-world performance of MIAs on diffusion models, we design and implement CopyMark, the first unified benchmark for MIAs on diffusion models. CopyMark distinguishes itself from previous evaluation from the following three aspects: 1) CopyMark is built on pre-trained diffusion models with no over-training and member and non-member datasets without dataset shift, which overcome these two defects of previous evaluation (Section 4.1); 2) CopyMark conducts blind evaluation on a test dataset other than the validation dataset used to find the threshold or train the classifier, which examines how MIAs perform on a blind test (Section 4.2); 3) CopyMark is implemented on diffusers, the state-of-the-art inference framework for diffusion models, making it flexible to generalize to new diffusion models (Section 4.3)

**Table 2: Five evaluation setups in CopyMark. (a) and (b) are defective setups from previous evaluation. (c), (d), and (e) are novel setups with no over-training and minor or no dataset shift.**
| Setup | Model | Member | Non-member | Dataset Shift | Dataset Size (k) | Epochs | Over-training |
| --- | --- | --- | --- | --- | --- | --- | --- |
| (a) | LDM | CelebA | FFHQ | ✓ | 50 | 500 | ✓ |
| (b) | SD1.5 | LAION | MS-COCO | ✓ | $\sim$600,000 | 1 | ✗ |
| (c) | SD1.5 | LAION | LAION | ✗ | $\sim$600,000 | 1 | ✗ |
| (d) | CommonCanvas-XL | CommonCatalog | MS-COCO | ✓(minor) | $\sim$2,500 | 1 | ✗ |
| (e) | Kohaku-XL | Hakubooru | Hakubooru | ✗ | $\sim$5,200 | 1 | ✗ |

### 4.1 Models and Datasets

Pre-trained diffusion models are the real-world interests of MIAs on diffusion models. Hence, we construct CopyMark on these pre-trained diffusion models. This covers the defect of over-training. However, it is non-trivial to select proper models for the evaluation of MIAs, because they must meet the following two requirements: 1) The training dataset (member dataset) is accessible to the public, and 2) There exist candidate non-member datasets whose distributions are similar or identical to that of the training dataset. We find three pre-trained diffusion models that meet the above requirements. We detail these models and the choice of their member and non-member datasets as follows:

- •
Stable Diffusion v1.5 (Rombach et al., ): The most widely-used pre-trained diffusion model. Stable Diffusion v1.5 is trained for 1 epoch on LAION Aesthetic v2 5+ (Schuhmann et al., ; ). We follow Dubiński et al. () to choose LAION Multi Translated as the source of non-members. There is no dataset shift since both member and non-member datasets come from the same distribution of LAION-2B dataset. We denote this setup by (c).
- •
CommonCanvas-XL-C (^1^11[https://huggingface.co/common-canvas/CommonCanvas-XL-C](https://huggingface.co/common-canvas/CommonCanvas-XL-C)) (Gokaslan et al., ): A pre-trained diffusion model in the architecture of SDXL (Podell et al., ). CommonCanvas-XL-C is trained for 1 epoch on CommonCatalog (Gokaslan et al., ), a large dataset consisting of multi-source Creative Commons licensed images. CommonCanvas-XL-C uses MS-COCO2017 as its validation dataset for generation performance. This inspires us to pick its non-members from MS-COCO2017. However, these member and non-member datasets have dataset shift because of the distribution difference between CommonCatalog and MS-COCO2017. We will show that this shift is minor. We denote this setup by (d).
- •
Kohaku-XL-Epsilon (^2^22[https://huggingface.co/KBlueLeaf/Kohaku-XL-Epsilon](https://huggingface.co/KBlueLeaf/Kohaku-XL-Epsilon)) (YEH et al., ): An SDXL fine-tuned on 5.2 millions of comic images from HakuBooru dataset (YEH et al., ) for 1 epoch. We follow the instruction in the homepage to separate HakuBooru dataset into the training dataset and the rest hold-out dataset. Then, we pick members from the training dataset and non-members from the hold-out dataset. As members and non-members are randomly picked from the same dataset, there is no dataset shift in Kohaku-XL-Epsilon. We denote this setup by (e).

Additionally, we also implement two previous defective setups in CopyMark: (a) LDM + CelebA (member) & FFHQ (non-member) (Fu et al., ) and (b) LDM + LAION (member) & MS-COCO2017 (non-member) (Duan et al., ; Kong et al., ). These two setups serve as a reference to our three new setups and also validate the correct of our implementation of MIA methods. The sanity check of datasets is discussed in Appendix A.1. All setups are summarized in Table 2.

Next, we review whether there are over-training and dataset shift in these setups:

Is there over-training? All of three pre-trained diffusion models are trained for only 1 epoch on every data point. Hence, there is no over-training in these three models.

Is there a dataset shift? We conduct an experiment to investigate the distribution shift between members and non-members for the above three setups. Specifically, we use CLIP (Radford et al., ) to extract semantic representations for images in the member dataset and the non-member dataset. Then, we visualize the CLIP embeddings of members and non-members by dimension compression and use an optimal hyper-plane to classify them.

Figure 1 demonstrates the visualization of semantic representations, while Table 3 posts the result of classification. Two defective setups, (a) and (b), have their members and non-members entirely distinguishable by CLIP embeddings. Quantitatively, the optimal hyper-plane achieves the true positive rate of 0.880-0.953 and the true negative rate of 0.818-0.963 in separating members and non-members of (a) and (b). In contrast, we can hardly discriminate members and non-members of (c), (d), and (e) by CLIP embeddings. It is noticeable that the optimal hyper-plane in (d) has a true positive rate of 0.690/0.606, indicating that members and non-members of (d) are slightly distinguishable by CLIP embeddings. This validates our above statement that there is a dataset shift in (d). However, this dataset shift is much more minor than those in (a) and (b). Hence, we still consider (d) as a qualified setup.

To conclude, our three new evaluation setups, (c), (d), and (e), have no over-training and minor or no dataset shifts. This is the main progress made by CopyMark compared to previous evaluation of MIAs on diffusion models.

Figure: Figure 1: Visualizing compressed CLIP embeddings of members and non-members of our 5 evaluation setups. (a) and (b), two defective setups, have their members and non-members markably distinguishable. In contrast, members and non-members of other three new setups, (c), (d) and (e), cannot be well separated in the CLIP embedding space.
Refer to caption: extracted/5902487/figs/clip_embedding_eval.png

**Table 3: Using hyper-plane in 3-D space to separate the compressed CLIP embeddings of members and non-members. High TPRs and TNRs show that members and non-members in defective Setup (a) and Setup (b) can be easily separated, indicating there are severe dataset shifts in these two setups. In our novel setups (c), (d), and (e), there are only minor or no dataset shifts, indicated by the TPRs and TNRs around $0.5$. Our new setups fit the real-world MIA scenario better.**
| Setup | (a) | (b) | (c) | (d) | (e) |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | Val | Test | Val | Test | Val | Test | Val | Test | Val | Test |
| TPR | 0.953 | 0.946 | 0.880 | 0.905 | 0.540 | 0.534 | 0.690 | 0.606 | 0.586 | 0.543 |
| FPR | 0.037 | 0.073 | 0.182 | 0.154 | 0.483 | 0.496 | 0.458 | 0.441 | 0.420 | 0.414 |
| TNR | 0.963 | 0.927 | 0.818 | 0.846 | 0.517 | 0.504 | 0.542 | 0.559 | 0.580 | 0.586 |
| FNR | 0.047 | 0.054 | 0.120 | 0.095 | 0.460 | 0.466 | 0.310 | 0.394 | 0.414 | 0.457 |

### 4.2 Two-stage Evaluation with Validation Datasets and Test Datasets

MIA methods on diffusion models need to use a dataset to find the optimal threshold or train the classifier (see Section 2.2 for explanation). However, previous evaluation of MIA methods only posts the result (TPR at $X\%$ FPR and AUC) on the same dataset. This raises doubts on the generalizability of these MIA methods. We propose to complement this drawback by introducing an extra dataset called test dataset.

Specifically, CopyMark randomly picks two groups of data with the same number of members and non-members from the source. We denote one by the validation dataset and the other by the test dataset. Our evaluation pipeline has two stages. The first stage is the same as previous evaluation, that we use the validation dataset to search for the optimal threshold to calculate TPR at $X\%$ FPR and AUC or train the classifier. The second stage is different, that we test the optimal threshold or the trained classifier on the test dataset. Since the test dataset does not involve in searching the optimal threshold or training the classifier, the second stage can be viewed as a blind test to the threshold or the classifier. It is noticeable that we can only post the TPR and FPR by the optimal threshold or the trained classifier on the test dataset. We summarize our two evaluation stages in Algorithm 1 and Algorithm 2.

Figure: Algorithm 1 The first stage (previous)

### 4.3 Implementation

Previously, there is no unified benchmark for MIAs on diffusion models. To fill this blank, we implement all state-of-the-art baseline methods of MIAs on diffusion models in CopyMark. We base our implementation on diffusers (von Platen et al., ), the state-of-the-art inference framework for diffusion models. We discuss the details of our implemention by points:

diffusers diffusers provides a unified API for running different diffusion models. We implement MIA methods as pipeline objects in diffusers. This enables MIA methods to generalize swiftly to different diffusion models. While diffusers is updated to support newly released diffusion models, CopyMark can benefit from the update and provide straight-forward generalization of MIAs to new diffusion models. This is the main advantage of implementing CopyMark on diffusers. We omit other implementation details to Appendix A.1.

Evaluation Metrics Following Duan et al. (), we randomlyy pick 2500 images as members and 2500 images as non-members. We repeat this picking twice to produce one validation dataset and one test dataset. For the validation dataset, we follow Carlini et al. () post TPR at $1\%$ FPR and $0.1\%$ together with the AUC (Algorithm 1). For the test dataset, we post the TPR and FPR for two optimal thresholds (the threshold at $1\%$ FPR and that at $0.1\%$ FPR) obtained from the validation set (Algorithm 2). The random seed of all evaluation is fixed for full reproducibility.

Baselines Duan et al. (); Fu et al. () show that general MIA methods do not work well in diffusion models. Hence, our baselines consist of MIA methods on diffusion models, including SecMI (Duan et al., ), PIA (Kong et al., ), PFAMI (Fu et al., ), GSA1 (Pang et al., ), and GSA2 (Pang et al., ). SecMI, PIA, and PFAMI are loss-based MIA methods, while GSA1 and GSA2 are classifier-based MIA methods. In addition to these MIA methods, we follow (Das et al., ) to implement a Blind baseline. This blind baseline trains a ConvNext (Liu et al., ) to classify members and non-members. We omit the details of baseline implementation to Appendix A.1.

**Table 4: Benchmark results of MIA methods on CopyMark. Red means FPR on the test set is higher than FPR upper-bound $X\%$ on the evaluation set.**
|  | (a) Latent Diffusion Model (CelebA-HQ $/$ FFHQ) |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
|  | Evaluation Set | Test Set |  |  |  |  |  |
|  | TPR@1%FPR | TPR@0.1%FPR | AUC | TPR1% | FPR1% | TPR0.1% | FPR0.1% |
| SecMI | 0.0728 | 0.0028 | 0.6131 | 0.0696 | 0.0084 | 0.0012 | 0.0004 |
| PIA | 0.0228 | 0.0016 | 0.6250 | 0.0252 | 0.0100 | 0.0004 | 0.0004 |
| PFAMI | 0.4988 | 0.2036 | 0.9172 | 0.5016 | 0.0192 | 0.1916 | 0.0012 |
| GSA1 | 1.0000 | 1.0000 | 1.0000 | 0.9516 | 0.0120 | 0.9516 | 0.0120 |
| GSA2 | 1.0000 | 1.0000 | 1.0000 | 0.9492 | 0.0132 | 0.9492 | 0.0132 |
| Blind | 1.0000 | 1.0000 | 1.0000 | 0.9932 | 0.0092 | 0.9932 | 0.0092 |
|  | (b) Stable Diffusion v1.5 (LAION Aesthetic V2 5+ $/$ MS-COCO2017) |  |  |  |  |  |  |
|  | Evaluation Set | Test Set |  |  |  |  |  |
|  | TPR@1%FPR | TPR@0.1%FPR | AUC | TPR1% | FPR1% | TPR0.1% | FPR0.1% |
| SecMI | 0.2888 | 0.1364 | 0.6991 | 0.3096 | 0.0084 | 0.1508 | 0 |
| PIA | 0.3120 | 0.1776 | 0.7617 | 0.3420 | 0.0112 | 0.1912 | 0 |
| PFAMI | 0.2124 | 0.1048 | 0.5870 | 0.2068 | 0.0072 | 0.1004 | 0 |
| GSA1 | 1.0000 | 1.0000 | 1.0000 | 0.8592 | 0.0968 | 0.8592 | 0.0968 |
| GSA2 | 1.0000 | 1.0000 | 1.0000 | 0.8556 | 0.0844 | 0.8556 | 0.0844 |
| Blind | 1.0000 | 1.0000 | 1.0000 | 0.9004 | 0.1156 | 0.9004 | 0.1156 |
| (c) Stable Diffusion v1.5 (LAION-Members $/$ LAION-Non-members) |  |  |  |  |  |  |  |
|  | Evaluation Set | Test Set |  |  |  |  |  |
|  | TPR@1%FPR | TPR@0.1%FPR | AUC | TPR1% | FPR1% | TPR0.1% | FPR0.1% |
| SecMI | 0.0128 | 0.0020 | 0.5231 | 0.0108 | 0.0088 | 0.0004 | 0.0004 |
| PIA | 0.0128 | 0.0020 | 0.5352 | 0.0124 | 0.0088 | 0.0004 | 0.0004 |
| PFAMI | 0.0156 | 0.0032 | 0.5101 | 0.0104 | 0.0108 | 0.0016 | 0.0020 |
| GSA1 | 1.0000 | 1.0000 | 1.0000 | 0.7016 | 0.2704 | 0.5608 | 0.4184 |
| GSA2 | 1.0000 | 1.0000 | 1.0000 | 0.6680 | 0.2736 | 0.5780 | 0.4056 |
| Blind | 0.9968 | 0.9520 | 0.6848 | 0.4592 | 0.3938 | 0.1432 | 0.1124 |
|  | (d) CommonCanvas-XL-C (CommonCatalog-CC-BY $/$ MS-COCO2017) |  |  |  |  |  |  |
|  | Evaluation Set | Test Set |  |  |  |  |  |
|  | TPR@1%FPR | TPR@0.1%FPR | AUC | TPR1% | FPR1% | TPR0.1% | FPR0.1% |
| SecMI | 0.0092 | 0.0004 | 0.5000 | 0.0080 | 0.0060 | 0 | 0 |
| PIA | 0.0124 | 0.0004 | 0.5184 | 0.0172 | 0.0084 | 0 | 0 |
| PFAMI | 0.0124 | 0.0004 | 0.5034 | 0.0208 | 0.0132 | 0 | 0 |
| GSA1 | 1.0000 | 1.0000 | 1.0000 | 0.8912 | 0.3132 | 0.8912 | 0.3132 |
| GSA2 | 1.0000 | 1.0000 | 1.0000 | 0.8880 | 0.1052 | 0.8880 | 0.1052 |
| Blind | 0.9984 | 0.9568 | 0.9998 | 0.8804 | 0.1564 | 0.7348 | 0.0624 |
| (e) Kohaku-XL-Epsilon (HakuBooru-Members $/$ HakuBooru-Non-members) |  |  |  |  |  |  |  |
|  | Evaluation Set | Test Set |  |  |  |  |  |
|  | TPR@1%FPR | TPR@0.1%FPR | AUC | TPR1% | FPR1% | TPR0.1% | FPR0.1% |
| SecMI | 0.0116 | 0.0169 | 0.5008 | 0.0116 | 0.0000 | 0.0136 | 0 |
| PIA | 0.0076 | 0 | 0.5051 | 0.0096 | 0.0128 | 0 | 0 |
| PFAMI | 0.0104 | 0.0008 | 0.4979 | 0 | 0 | 0 | 0 |
| GSA1 | 1.0000 | 1.0000 | 1.0000 | 0.5668 | 0.4192 | 0.5668 | 0.4192 |
| GSA2 | 1.0000 | 1.0000 | 1.0000 | 0.5536 | 0.4292 | 0.5536 | 0.4292 |
| Blind | 0.9736 | 0.9584 | 0.9997 | 0.4204 | 0.3064 | 0.3528 | 0.2444 |

## 5 Results: MIAs on Diffusion Models Fail on Real-World Setups

We use five setups in CopyMark to evaluate state-of-the-art MIA method on diffusion models and show the result in Table 4. Unfortunately, while they perform consistently with the result in the original papers on the previous setups, all MIA methods fail on our new real-world setups.

MIAs perform consistently with results in the original papers We compare our results on setup (a) and (b) to the results in the original paper of MIA methods to cross-validate the correctness of our implementation. In the original paper of PFAMI (Fu et al., ), its AUC on setup (a) is 0.961, while our result is 0.9172. Our result is slightly lower than the original result. However, both result are in the same level. In the original paper of SecMI (Duan et al., ) and PIA (Kong et al., ), the TPRs@$1\%$FPR are 0.1858 and 0.198, and the AUCs are 0.701 and 0.739, respectively. Our results are 0.3120 and 0.2888 for the TPR@$1\%$FPR and 0.7617 and 0.6991 for the AUC, which are slightly better. The slight difference between our results and the original results are acceptable and should be attributed to the different in random seed and dataset sampling. The consistent performance of baselines on setup (a) and (b) validates the correctness of our implementation.

Loss-based MIAs fail on real-world setups On setup (c), (d), and (e), however, loss-based MIA methods (SecMI, PIA, and PFAMI) are absolutely failed. Their TPRs@$1\%$FPR and TPRs@$0.1\%$FPR are close to the FPR threshold, indicating that they are not able to distinguish even a few members from non-members.

Classifier-based MIAs fail on real-world setups Compared to loss-based MIAs, classifier-based MIAs (GSA1 and GSA2) perform better on three real-world setups. GSA1 and GSA2 always succeed in separating members and non-members in the validation dataset because they exploit the classifier trained on the same dataset. However, when transferring the classifier to the test dataset, the performance degrades significantly. First, the TPRs drop to the range of $0.55-0.89$. Second, the FPRs rise dramatically to the range of $0.10-0.43$, much higher than the original FPR of the threshold. We use red number to note the test FPRs higher than the validation FPRs. In other word, classifier-based MIAs tend to classify $10\%-40\%$ of the non-members as members. Therefore, they cannot be trustworthy evidence of diffusion model membership either.

Blind baseline beats loss-based MIAs It is noticeable that the Blind baseline, based on a ConvNext classifier, yields competitive performance. On setups (a) and (b), it outperforms all MIA methods. This again indicates the defect of these previous evaluation setups because they can be totally covered without accessing to the diffusion model. On our real-world setups (c), (d), and (e), the blind baseline beats loss-based MIAs with a similar performance to that of classifier-based MIAs. This proves that classifier-based methods have some practical value. It also shows that our setups require the methods to depend more on the membership rather than the distribution shift between members and non-members, which is our superiority. We believe that all future MIA methods should be compared to this blind baseline in the evaluation.

Loss-based MIAs generalize better than classifier-based MIAs Throughout all five setups, we notice that loss-based MIAs have good generalizability, that they perform consistently on test datasets as on validation datasets. They seldom yield a test FPR higher than the FPR of validation threshold. In contrast, classifier-based MIAs suffer from the performance gap between validation datasets and test datasets. This difference in generalizability is straight-forward to understand: Classifier-based MIAs depends on a neural network that tends to over-fit the features of data points to achieve the perfect performance on the validation dataset. This over-fitting results in performance degradation on the test dataset. To eliminate this problem, we must further refine the feature selection.

## 6 Discussion

Section 5 shows the failure of current diffusion MIAs on real-world benchmarks. In this section, we provide intuitive ideas on the possible reason and improvements of current MIAs. We also discuss the potential of using MIAs as evidence in AI copyright lawsuits.

### 6.1 Why do current MIAs fail on Pre-trained Diffusion Models?

Two kinds of MIAs, loss-based MIAs (Duan et al., ; Kong et al., ; Fu et al., ) and classifier-based MIAs (Pang et al., ), fail for different reasons:

Loss-based MIAs: These methods are built on the hypothesis that training losses of members are lower than those of non-members. However, pre-trained diffusion models were trained on one data point for one iteration. Hence, the difference between member training losses and non-member training losses are smaller. Also, the training loss depends implicitly on the Gaussian noise added to the data point. While the training loss is calculated as an expectation over the whole time scheduling and the whole Gaussian noise space, its variance may grow bigger than the difference between member training losses and non-member training losses. This inevitable mechanism always exposes loss-based MIAs under the risk of failure. To overcome this, future research on loss-based MIAs need to develop more powerful functions in distinguishing the losses of members and non-members.

Classifier-based MIAs: The failure of classifier-based MIAs originates from over-fitting of the classifier. Currently, features of data points are not sufficient for predicting the membership. Meanwhile, classifier parameters are always redundant. These induce the classifier to over-fit the features. However, the bottleneck may be overcome in the future by refining feature selection and training setups. This could be a potential direction to improve MIAs on diffusion models.

### 6.2 Are MIAs potential evidence of unauthorized data usage in AI lawsuits?

Recent progress in AI copyright lawsuits (Andersen, ; Zhang, ) indicates the necessity of evidence of unauthorized data usage in pre-trained diffusion models. Specifically, the plaintiff claims that pre-trained diffusion models copy their copyright images without authorization and expects to get evidence of this copying by MIAs on diffusion models. According to copyright laws (U.S. Copyright Office, ; European Parliament and Council, ), however, the proof of copying requires showing substantial similarity between the defendant’s work and original elements of the plaintiff’s work. In the context of AI copyright lawsuits, this means that the plaintiff must provide images generated by pre-trained diffusion models with content similarities to their copyright images. Unfortunately, today’s MIAs could only give binary membership indicators as outputs. Moreover, as shown in this paper, current MIAs on diffusion models are not reliable tools to even indicate membership. Hence, it is non-realistic to make use of MIAs as evidence in AI copyright lawsuits.

## 7 Additional Related Works

We are the first to validate and alert the defect in the evaluation of MIAs on diffusion models. Some works reported similar risks in MIAs on Large Language Models (Das et al., ; Maini et al., ). Liu & He () shows that most vision dataset pairs could be classified by a simple classifier, which inspires our investigation to the previous evaluation of MIAs on diffusion models. Our unified benchmark for MIAs on diffusion models covers the dataset for real-world evaluation of MIAs in Dubiński et al. (). However, they do not implement any MIA methods on their dataset.

## 8 Conclusion

In this paper, we reveal two defects in the previous evaluation of membership inference attacks (MIAs) on diffusion models: over-training and dataset shifts, which result in overestimate of MIAs’ performance. To overcome these defects, we propose CopyMark, the first unified benchmark for MIAs on diffusion models. Our choice of models and datasets keeps CopyMark away from over-training and dataset shifts. We evaluate existing MIA methods with CopyMark and find that current MIAs on diffusion models fail in real-world scenarios of MIA. We alert that MIAs on diffusion models are not trustworthy tool to provide evidence for unauthorized data usage in diffusion models. This conclusion is significant for both future research in MIAs on diffusion models are for people involving AI copyright lawsuits.

## Appendix A Appendix

### A.1 Implementation Details

diffusers diffusers abstracts inference workflows of diffusion models as pipelines. A pipeline loads and manages Modules of diffusion models. Then, it takes inputs and returns outputs. For example, StableDiffusionImage2ImagePipeline takes images and text prompts as inputs and uses modules of Stable Diffusion to sample output images with SDEdit (Meng et al., ). Usually, state-of-the-art diffusion models consist of three modules: U-Net (UNet2DModel), VAE (AutoencoderKL), and text encoder (CLIPTextModel (Radford et al., )). One diffusion model only have one set of modules. However, it may have several different pipelines. For example, StableDiffusionImg2ImgPipeline (Meng et al., ), StableDiffusionInstructPix2PixPipeline (Brooks et al., ), and StableDiffusionGLIGENPipeline (Li et al., ) are all pipelines of Stable Diffusion v1.5.

Baselines We first introduce the idea of our baselines as follows:

- •
SecMI (Duan et al., ): A loss-based method. SecMI uses a parameterized forward step $p_{\theta}(x_{t}|x_{t-1},x_{0})$ to predict $x_{t}$ from $x_{t-1}$. Then, it applies a reverse step $p_{\theta}(x_{t}|x_{t-1},x_{0})$ to predict $\widetilde{x}_{t-1}$. The score is given by the $l_{2}$ distance between $x_{t-1}$ and $\widetilde{x}_{t-1}$, that diffusion models should better predict $x_{t-1}$ for member images. SecMI use the distance at $t=50$, while we also try a variant that uses the distance at different $t$, termed by SecMI++.
- •
PIA (Kong et al., ): A loss-based method. PIA distinguishes member data by checking how diffusion models denoise the $x_{t}$ with the same noise $\epsilon_{0}$. The score is given by the loss computed over different timesteps $t$.
- •
PFAMI (Fu et al., ): A loss-based method. PFAMI exploits the loss fluctuation in the image neighborhood. The neighborhood of image $x$ refers to images that share similar contents with $x$ and is constructed by cropping $x$. It compares the loss of $x$ with that of its neighborhood. It assumes that the loss of non-member images approximates those of their neighborhood images, while the loss of member images should be a distinct local minimum among those of the neighborhood images.
- •
GSA (Pang et al., ): The first gradient-based method. GSA aggregates gradients on modules in diffusion models over different timesteps $t$ and uses the $l_{2}$ norm of these gradients as features. Then, it trains an XGBoost (Chen & Guestrin, ) binary classifier to discriminate features from member data and those from non-member data. The score is given by the classifier. GSA has two variants, termed by GSA1 and GSA2.

All baselines are implemented based on their official open-sourced implementation. For SecMI, we use DDIM (Song et al., ) as the sampling method with $\eta=0$ and pick the score at $t=50$ as advised by the official implementation (^3^33[https://github.com/jinhaoduan/SecMI-LDM](https://github.com/jinhaoduan/SecMI-LDM)). For PIA, we follow the official implementation (^4^44[https://github.com/kong13661/PIA](https://github.com/kong13661/PIA)) to compute losses at $t\in\{0,10,20,...,480\}$. For PFAMI, we follow the original setup in the official implementation (^5^55[https://anonymous.4open.science/r/MIA-Gen-5F40/](https://anonymous.4open.science/r/MIA-Gen-5F40/)) to set the neighbor number $N$ as 10, the attacking number $M$ as 1, and the interval of perturbation strengths as $[0.75,0.9]$. For the above methods, we separate the threshold interval $[\tau_{min},\tau_{max}]$ in Algorithm 1 into 10,000 sub-intervals and pick the corresponding 10,000 lower-bounds for optimal threshold searching. For GSA1 and GSA2, we use the default setup (^6^66[https://github.com/py85252876/GSA](https://github.com/py85252876/GSA)) to compute losses (GSA1) or gradients (GSA2) over different modules at $t\in\{0,50,100,...,1000\}$. An XGBoost (Chen & Guestrin, ) classifier with 200 estimators is trained on the gradients to distinguish member images, following the original implementation. The threshold of GSA1 and GSA2 is fixed to 0.5 because the XGBoost classifier outputs binary scores of $\{0,1\}$. For all methods, we use the seed function from the official implementation of SecMI (^7^77[https://github.com/jinhaoduan/SecMI-LDM/blob/secmi-ldm/src/mia/secmi.py](https://github.com/jinhaoduan/SecMI-LDM/blob/secmi-ldm/src/mia/secmi.py)) that fixes the seed as 1 to make the result deterministic.

Sanity Check Setup (a) and (b) are mirroring setups of previous evaluation setups (Duan et al., ; Fu et al., ). Hence, we do not repeat their sanity checks. The sanity check of setup (c) has been done by Dubiński et al. (). For Setup (d), CommonCanvas-XL-C uses MS-COCO2017 as its validation set for generation performance (Gokaslan et al., ). This indicates that MS-COCO2017 is held out of the training dataset of CommonCanvas-XL-C. In Setup (e), every data point in HakuBooru dataset has a unique ID, which the author of Kohaku-XL-Epsilon used to select the training dataset from the whole dataset. We follow the instruction in the homepage (^8^88[https://huggingface.co/KBlueLeaf/Kohaku-XL-Epsilon](https://huggingface.co/KBlueLeaf/Kohaku-XL-Epsilon)) to randomly pick images from the ID range of the training dataset as members and images out of this ID range as non-members. Hence, there should be no overlap between members and non-members.

**Table 5: Complexity analysis and running time for MIA methods. Query (FP) and Query (BP) are the number of forward propagations and back propagation the method conducts per image. Running time is given based on the whole experiments of 2500 images on three models: Latent Diffusion, Stable Diffusion v1.5, and CommonCanvas-XL-C. Experiments are conducted on an NVIDIA A100 GPU.**
|  | Query (FP) | Query (BP) | Time (LDM) | Time (SD) | Time (CC-XL-C) |
| --- | --- | --- | --- | --- | --- |
| SecMI | 100 | 0 | 2339 | 8965 | 16280 |
| PIA | 100 | 0 | 2804 | 9331 | 20397 |
| PFAMI | 1100 | 0 | 47171 | 40787 | 47909 |
| GSA1 | 20 | 1 | 5886 | 12787 | 18146 |
| GSA2 | 20 | 20 | 6729 | 14143 | 26771 |

Computational resources All experiments are finished on $2\times$ NVIDIA A100 80GB GPUs.

### A.2 Codebase of CopyMark on diffusers

The codebase of CopyMark on diffusers mainly consists of three parts: diffusers pipeline, data and evaluation utilities, and training scripts.

diffusers pipelines We implements every MIA method as a pipeline in diffusers. Pipelines of one diffusion model (e.g. Stable Diffusion) are consistently inherited from the model’s text-to-image pipeline (StableDiffusionPipeline for Stable Diffusion and StableDiffusionXLPipeline for SDXL) or the unconditional generation pipeline (DiffusionPipeline for Latent Diffusion Models). These pipelines load modules with the unified module loading API of diffusers. They differs from the parent pipeline only by the __call__() function. We modify their __call__() to take images as inputs and return the result as outputs. We list all pipelines implemented as follows:
{python}
SecMILatentDiffusionPipeline
SecMIStableDiffusionPipeline
SecMIStableDiffusionXLPipeline
PIALatentDiffusionPipeline
PIAStableDiffusionPipeline
PIAStableDiffusionXLPipeline
PFAMIMILatentDiffusionPipeline
PFAMIStableDiffusionPipeline
PFAMIStableDiffusionXLPipeline
GSALatentDiffusionPipeline
GSAStableDiffusionPipeline
GSAStableDiffusionXLPipeline
SecMI & SecMI++ and GSA1 & GSA2 share one pipeline respectively with different arguments.

Data and evaluation utilities Since all pipelines take images as inputs and return scores as outputs, we use a set of unified utilities to load the images and optimize the threshold from the scores.

Training scripts The training script of one MIA method assembles the diffusers pipeline and the utilities. It first loads images and text prompts with the data utility. Then, it employs the diffusers pipeline to calculate scores. Finally, it uses the evaluation utility to optimize the threshold according to the scores and evaluate the threshold.

### A.3 Additional Related Works

Unauthorized data usage of diffusion models have been a crucial topic that raises increasing attention (Franceschelli & Musolesi, ; Sag, ; Samuelson, ). One popular approach to relieve the concern of unauthorized data usage in diffusion models is to add adversarial (Salman et al., ; Shan et al., ; Liang et al., ; Liang & Wu, ; Van Le et al., ; Shan et al., ; Xue et al., ) or copyright watermarks (Cui et al., ; Zhu et al., ) to images. These watermarks either resist diffusion models from training on the image or introduce copyright information to diffusion models trained on the image. However, recent research questions the effectiveness of these watermarks that they might be failed easily (Zhao et al., ). Another recipe is to erase or unlearn the copyright data in the diffusion model (Gandikota et al., ; Zhang et al., ; Fan et al., ; Wu et al., ; Zhang et al., ). Nevertheless, Zhang et al. () shows that current machine unlearning on diffusion models can be bypassed by soft prompting and other fine-tuning methods. As protective and post-training refining methods are faced with questioning, we highlight the potential to directly detect copyright data in the training dataset of diffusion models, by which we help the calling for copyright protection beyond technical methods.

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: See Weakness part.
soundness: 3
strengths: - The writing is clear
- The structure is easy to follow
- The paper considered comprehensive comparison with the relate works
summary: The paper introduces a straightforward yet powerful benchmark to assess the performance of existing Membership Inference Attacks (MIA) on pre-trained diffusion models within the context of data authorization. The authors identified "overtraining" and "dataset shifts" as two significant limitations of current MIA methods. To address these issues, they developed a benchmark featuring five experimental setups.
weaknesses: - I am unsure about the input for the membership inference attacks. In Lines 113-116, does x refer solely to the image, or is it a combination of the image and its prompt? I recommend that the authors clarify this in the problem setup.

- In Table 1, why does "LDM + CelebA" have $\times$ for both “Over-training” and “Shifted Datasets,” while in the bottom table, "LDM + CelebA" (i.e., the third row) has $\checkmark$ for both? Is this a typo, or have I misunderstood the notation?

- While I appreciate the authors’ efforts in benchmarking MIA methods in practical scenarios, I believe the paper’s analysis of the two challenges, “Over-training” and “Shifted Datasets,” could be more in-depth. For example, I recommend adding an analysis of how shifted datasets impact MIA performance based on the distance of non-members from the target data (e.g., considering extremely close, moderately distant, and far distant non-members).

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: See weakness.
soundness: 3
strengths: - Presentation is good and easy to follow.
- The addressed problem is meaningful.
summary: The paper proposed a simple but effective benchmark for evaluating the existing MIA’s performance on the pre-trained diffusion models for the data authorization problem. The authors first found that “overtraining” and “dataset shifts” are two major defects of the existing MIA methods. Then, to overcome the two challenges, the authors proposed a benchmark that incorporates five different experimental setups, where the last three avoids the dataset shifting problem by using members and non-members from the same distributions, and over-training problem by only considering pre-trained models training for 1 epoch.
weaknesses: - I am confused about the upper part of Table 1. What do the “✅” and “❌” symbols represent in each entry? Additionally, are “Over-training” and “Shifted Datasets” considered issues in each experimental setup (e.g., is over-training a problem in the DDPM + CIFAR10 setup)? If so, why is over-training necessarily a problem for DDPM + CIFAR10? I believe this only holds when certain factors, like training epochs, are fixed as you reported in the common setting; otherwise, this claim seems overstated.

- Could the benchmark allow for more varied experimental setups—for instance, having no dataset shift but including over-training? A simple example could involve training a DDPM on the CIFAR10 training set and using the CIFAR10 test set as non-members, which would meet the no-shift criterion.

- Furthermore, the concept of “dataset shift” is somewhat unclear to me. The benchmark assumes there’s no distribution shift when two datasets come from the same source. I suggest the authors delve deeper into this by considering metrics to quantify dataset distance (distribution distance), such as the Wasserstein distance.

---

confidence: 3
contribution: 3
initial_rating: 6
presentation: 3
questions: The paper aims to construct a real-world benchmark, pinpointing the current limitation of MIA setups, specifically the unknown distribution of members and non-members in real-world MIAs. It is reasonable that a newly proposed benchmark can cause current methods to yield poor performance. However, I find the discussion lacking in adequately demonstrating how this benchmark accurately reflects real-world settings from my perspective. In my opinion, additional evidence and a more thorough discussion would strengthen this aspect.

In the evaluation setup part, the paper mentions that (d) has a slight data shift but is more minor than other settings. Can you provide further insight into how minor dataset shifts were quantified and their potential impact on the validity of MIA results? It would be beneficial to have a more detailed analysis of how significant these shifts need to be in impacting the effectiveness of MIAs. What thresholds for dataset similarity were considered, and how were they determined?

The paper demonstrates that current MIAs are less effective under realistic conditions on diffusion models. How do you envision these findings being applicable to other types of generative models? Are there specific characteristics of diffusion models that may limit the generalizability of the results? A discussion on this could clarify potential broader applications of your findings.

This paper conducts a comprehensive experiment and concludes that the current MIAs on diffusion models do not perform well in real-world scenarios. However, I think the discussion part is relatively superficial and requires a deeper analysis based on the experimental results. Can you provide more implications and extend the discussion to promote future research?
soundness: 3
strengths: 1. Good and significant topic. The paper identifies a critical gap in the evaluation of MIAs, offering a novel approach to benchmarking that could reshape how these attacks are studied, and providing valuable insights that can influence the future research.
2. Comprehensive experiment. The experiments conducted are extensive, providing evidence that challenges the overestimation of MIA effectiveness on diffusion models.
summary: The paper presents a novel approach to assessing MIA on diffusion models by introducing a new benchmark called CopyMark. This benchmark aims to provide a realistic and unbiased environment for testing the effectiveness of MIAs against these models. The study underscores the potential overestimation of MIA effectiveness due to biased experimental setups in previous research and argues for a more nuanced understanding and evaluation of MIAs in practical applications. The paper pinpoints that current MIAs on diffusion models are not trustworthy tool to provide evidence for unauthorized data usage in diffusion models.
weaknesses: 1. Lack of discussion. The discussion on the practical implications of the findings is somewhat superficial and lacks depth in Section 6, particularly in how these results could influence real-world security strategies.

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: 1. How do the issues of over-training and dataset shifts differ between diffusion models and traditional deep learning models or large language models? Will the proposed realistic scenarios similarly reduce MIA effectiveness on these other model types?

2. How do MIA methods based on likelihood and quantile regression perform on diffusion models in the proposed realistic scenarios? Will their performance also see a significant reduction?

3. Minor point: a typo “randomlyy” in the third paragraph of section 4.3.
soundness: 3
strengths: 1. The paper is well-written and easy to follow. It explains the flaws in existing MIA evaluations, i.e., over-training and dataset shifts, and is structured to understand these two problems through quantitative and qualitative analyses. 

2. This paper makes valuable thoughts about the limitations of current MIA evaluations on diffusion models. The significance of the proposed realistic evaluation for MIA is substantial, particularly in the context of AI copyright lawsuits and data privacy.
summary: This paper investigates the evaluation of state-of-the-art membership inference attacks (MIAs) on diffusion models in real-world scenarios. Specifically, it highlights flaws in current MIA evaluations, where over-training and dataset shifts lead to overestimated performance of the membership detection. To address this, the paper introduces a unified benchmark for MIAs on diffusion models, named CopyMark, which is built without over-training, using non-shifted datasets and blind testing. The experiments cover the recent loss-based MIA methods and classifier-based MIA methods, conducted on both defective setups and real-world setups. The results reveal that existing MIAs perform poorly on diffusion models in realistic scenarios.
weaknesses: 1. The originality of these two flaws, i.e., over-training and dataset shifts, remains a concern. Similar concepts like over-fitting and distribution shifts have been discussed in previous works (Carlini et al., 2022; Maini et al., 2024) on traditional deep learning models and large language models. This paper may potentially adapt the MIA setting to diffusion models while providing more assessments.

2. Although the paper assesses existing MIA methods on diffusion models, it does not explore possible adjustments to improve MIA performance on CopyMark. For example, how to address the challenges identified on existing loss-based and classifier-based MIA methods and how to achieve better results under realistic scenarios.

3. The evaluation may lack comprehensiveness as a benchmark, as the experiments are limited to loss-based and classifier-based MIA methods on diffusion models. Other types of MIAs, such as likelihood-based MIAs (Hu & Pang, 2023) and MIAs using Quantile Regression (Tang et al., 2024), are not included.

Carlini et al. Membership inference attacks from first principles. 2022 IEEE Symposium on Security and Privacy. 2022.

Maini et al. LLM Dataset Inference: Did you train on my dataset? arXiv preprint arXiv:2406.06443. 2024.

Hu & Pang. Loss and likelihood based membership inference of diffusion models. In International Conference on Information Security. 2023.

Tang et al. Membership inference attacks on diffusion models via quantile regression. International Conference on Machine Learning. 2024.

Meta-review: The paper aims to evaluate the state-of-the-art MIAs on diffusion models and reveal critical flaws and overly optimistic performance estimates in existing MIA evaluation. The presentation is clear and the experiments are also good. Reviewers like this paper, but find many issues that can not be easily fixed in a short time, such as the lack of discussion and the lack of the evaluation and so on.

Decision: Reject