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Diffusion Sensitivity Geometry and Strong Duality for Optimal Privacy-Utility Tradeoffs

Tue Do, Daniel Alabi · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28991 · cited by 0 works (OpenAlex) · open-access PDF

Portuguese

As abordagens existentes para a privacidade diferencial em modelos de difusão baseiam-se em limites de sensibilidade soltos e ruído isotópico de Gauss, levando a erros de estimativa desnecessários. Desenvolvemos um quadro para o comércio de privacidade-utilidade ideal de detonadores de difusão, substituindo limites conservadores com características de sensibilidade exatas e provavelmente calibração de ruído ideal. Primeiro, mostramos que a sensibilidade do pior caso sobre conjuntos de dados de tamanho arbitrário pode ser caracterizada com exatidão usando apenas dois registros. Para um domínio de dados de tamanho $m$, isso reduz a análise para o máximo de $m(m-1)$ restrições de privacidade, independentemente do tamanho do conjunto de dados. Nossa caracterização pode ser arbitrariamente

Machine translation (Meta M2M100); the English original follows.

Abstract

Existing approaches to differential privacy in diffusion models rely on loose sensitivity bounds and isotropic Gaussian noise, leading to unnecessary estimation error. We develop a framework for the optimal privacy-utility tradeoff of ideal diffusion denoisers, replacing conservative bounds with exact sensitivity characterizations and provably optimal noise calibration. First, we show that worst-case sensitivity over datasets of arbitrary size can be characterized exactly using only two records. For a data domain of size $m$, this reduces the analysis to at most $m(m-1)$ constraints, regardless of dataset size. Our characterization can be arbitrarily tighter than conventional diameter-based sensitivity bounds, revealing potentially unbounded improvements in noise calibration. Second, we obtain exact privacy guarantees for Rényi, approximate, and Gaussian differential privacy, as well as mutual-information privacy for binary records, avoiding the looseness of previous generic privacy conversions. Finally, we show that the minimum achievable weighted mean-squared error can be computed through a semidefinite program and prove strong duality, providing certificates of global optimality.

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Topics: Sensitivity (control systems), Differential privacy, Duality (order theory), Gaussian, Mathematics, Noise (video)

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