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Gradient-Guided Conditional Diffusion Models for Private Image Reconstruction: Analyzing Adversarial Impacts of Differential Privacy and Denoising

Tao Huang, Jiayang Meng, Hong Chen, Guolong Zheng, Xu Yang, Xun Yi, Hua Wang

TL;DR

This work investigates the construction of gradient-guided conditional diffusion models for reconstructing private images, focusing on the adversarial interplay between differential privacy noise and the denoising capabilities of diffusion models to propose two novel methods that require minimal modifications to the diffusion model's generation process and eliminate the need for prior knowledge.

Abstract

We investigate the construction of gradient-guided conditional diffusion models for reconstructing private images, focusing on the adversarial interplay between differential privacy noise and the denoising capabilities of diffusion models. While current gradient-based reconstruction methods struggle with high-resolution images due to computational complexity and prior knowledge requirements, we propose two novel methods that require minimal modifications to the diffusion model's generation process and eliminate the need for prior knowledge. Our approach leverages the strong image generation capabilities of diffusion models to reconstruct private images starting from randomly generated noise, even when a small amount of differentially private noise has been added to the gradients. We also conduct a comprehensive theoretical analysis of the impact of differential privacy noise on the quality of reconstructed images, revealing the relationship among noise magnitude, the architecture of attacked models, and the attacker's reconstruction capability. Additionally, extensive experiments validate the effectiveness of our proposed methods and the accuracy of our theoretical findings, suggesting new directions for privacy risk auditing using conditional diffusion models.

Gradient-Guided Conditional Diffusion Models for Private Image Reconstruction: Analyzing Adversarial Impacts of Differential Privacy and Denoising

TL;DR

This work investigates the construction of gradient-guided conditional diffusion models for reconstructing private images, focusing on the adversarial interplay between differential privacy noise and the denoising capabilities of diffusion models to propose two novel methods that require minimal modifications to the diffusion model's generation process and eliminate the need for prior knowledge.

Abstract

We investigate the construction of gradient-guided conditional diffusion models for reconstructing private images, focusing on the adversarial interplay between differential privacy noise and the denoising capabilities of diffusion models. While current gradient-based reconstruction methods struggle with high-resolution images due to computational complexity and prior knowledge requirements, we propose two novel methods that require minimal modifications to the diffusion model's generation process and eliminate the need for prior knowledge. Our approach leverages the strong image generation capabilities of diffusion models to reconstruct private images starting from randomly generated noise, even when a small amount of differentially private noise has been added to the gradients. We also conduct a comprehensive theoretical analysis of the impact of differential privacy noise on the quality of reconstructed images, revealing the relationship among noise magnitude, the architecture of attacked models, and the attacker's reconstruction capability. Additionally, extensive experiments validate the effectiveness of our proposed methods and the accuracy of our theoretical findings, suggesting new directions for privacy risk auditing using conditional diffusion models.

Paper Structure

This paper contains 18 sections, 9 theorems, 44 equations, 7 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work and Preliminary
  3. Gradient Leakage and Image Reconstruction
  4. Diffusion Models and Conditional Diffusion Models
  5. Differential Privacy
  6. Reconstruction of Private Images
  7. Gradients as Condition Measures
  8. Adversarial Impacts of Differential Privacy and Conditional Denoising Diffusion Models
  9. Experiments
  10. Experimental Setup
  11. Results and Discussion
  12. Reconstructions Without Differentially Private Noise
  13. Impacts of Gaussian noise scale sigma2
  14. Vulnerability of Different Machine Learning Models.
  15. Impacts of Step Size and Guidance Rate
  16. ...and 3 more sections

Key Result

Lemma 1

Let $\mathcal{M}: \mathcal{D} \rightarrow \mathbb{R}^k$ be a function with $\ell_2$-sensitivity $\Delta_2 \mathcal{M} = \| \mathcal{M}(D) - \mathcal{M}(D^{\prime}) \|$ which measures the maximum change in the Euclidean norm of $\mathcal{M}$ for any two adjacent datasets $D$ and $D^{\prime}$ that dif

Figures (7)

  • Figure 1: Forward and reverse process of diffusion models
  • Figure 2: Explanations for Theorem \ref{['DSGlower']}
  • Figure 3: Reconstruction Processes
  • Figure 4: Images $x_{t}$ of Reconstruction Process
  • Figure 5: Reconstruction with noisy gradients.
  • ...and 2 more figures

Theorems & Definitions (17)

  • Definition 1: Differential privacy b28
  • Lemma 1: Gaussian Mechanism for Differential Privacy b28
  • Definition 2: Jensen Gap b19
  • Theorem 1: Upper Bound of Jensen Gap of Reconstruction Error
  • proof
  • Definition 3: Reconstruction Vulnerability of Machine Learning Models
  • Lemma 2
  • Lemma 3
  • Theorem 2: Lower bound of Jensen Gap of Reconstruction Error
  • proof
  • ...and 7 more