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《Towards Black-Box Membership Inference Attack for Diffusion Models》

Abstract

1. 识别艺术品是否用于训练扩散模型的挑战，重点是人工智能生成的艺术品中的成员推断攻击——copyright protection
2. 不需要访问内部模型组件的新型黑盒攻击方法
3. 展示了在评估 DALL-E 生成的数据集方面的卓越性能。

作者主张

previous methods are not yet ready for copyright protection in diffusion models.

Contributions（文章里有三点，我觉得只有两点）

1. ReDiffuse：using the model’s variation API to alter an image and compare it with the original one.
2. A new MIA evaluation dataset：use the image titles from LAION-5B as prompts for DALL-E’s API [31] to generate images of the same contents but different styles.

Algorithm Design

target model：DDIM

为什么要强行引入一个版权保护的概念？？？

定义black-box variation API

$$\hat{x}=V_{\theta }(x,t)$$

细节如下：

总结为：$x$加噪变为$x_t$，再通过DDIM连续降噪变为$\hat{x}$

intuition

Our key intuition comes from the reverse SDE dynamics in continuous diffusion models.

one simplified form of the reverse SDE (i.e., the denoise step)
$$X_t=(X_t/2-{\nabla }_x\log p(X_t))+d{W}_t,t\in [0,T]\text{\hspace{1em}(3)}$$

The key guarantee is that when the score function is learned for a data point x, then the reconstructed image ${\hat{x}}_i$ is an unbiased estimator of $x$.（算是过拟合的另一种说法吧）

Hence，averaging over multiple independent samples ${\hat{x}}_i$ would greatly reduce the estimation error (see Theorem 1).

On the other hand, for a non-member image $x^{\prime }$, the unbiasedness of the denoised image is not guaranteed.

details of algorithm：

1. independently apply the black-box variation API n times with our target image x as input
2. average the output images
3. compare the average result $\hat{x}$ with the original image.

evaluate the difference between the images using an indicator function:
$$f(x)=1[D(x,\hat{x})<\tau ]$$
A sample is classified to be in the training set if $D(x,\hat{x})$ is smaller than a threshold $\tau$ ($D(x,\hat{x})$ represents the difference between the two images)

ReDiffuse

Theoretical Analysis

什么是sampling interval？？？

MIA on Latent Diffusion Models

泛化到latent diffusion model，即Stable Diffusion

ReDiffuse+

variation API for stable diffusion is different from DDIM, as it includes the encoder-decoder process.
$$z=\mathrm{Encoder}(x),z_t=\sqrt{{\overline{\alpha }}_t}z+\sqrt{1-{\overline{\alpha }}_t}ϵ,\hat{z}={\Phi }_{\theta }(z_t,0),\hat{x}=\mathrm{Decoder}(\hat{z})\text{\hspace{1em}(4)}$$
modification of the algorithm

independently adding random noise to the original image twice and then comparing the differences between the two restored images ${\hat{x}}_1$ and ${\hat{x}}_2$:
$$f(x)=1[D({\hat{x}}_1,{\hat{x}}_2)<\tau ]$$

Experiments

Evaluation Metrics

1. AUC
2. ASR
3. TPR@1%FPR

same experiment’s setup in previous papers [5, 18].

target model	DDIM	Stable Diffusion
version	《Are diffusion models vulnerable to membership inference attacks?》	original：stable diffusion-v1-5 provided by Huggingface
dataset	CIFAR10/100，STL10-Unlabeled，Tiny-Imagenet	member set：LAION-5B，corresponding 500 images from LAION-5；non-member set：COCO2017-val，500 images from DALL-E3
T	1000	1000
k	100	10

baseline methods	[5]Are diffusion models vulnerable to membership inference attacks?: SecMIA	[18]An efficient membership inference attack for the diffusion model by proximal initialization.	[28]Membership inference attacks against diffusion models
publication	International Conference on Machine Learning	arXiv preprint	2023 IEEE Security and Privacy Workshops (SPW)

Ablation Studies

1. The impact of average numbers
2. The impact of diffusion steps
3. The impact of sampling intervals