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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

Indonesian

Pendekatan yang ada untuk privasi diferensial dalam model difusi bergantung pada batas sensitivitas yang longgar dan kebisingan Gaussian isotropik, yang mengarah pada kesalahan perkiraan yang tidak perlu. Kami mengembangkan kerangka kerja untuk pertukaran privasi-manfaat yang optimal dari denoisers difusi ideal, menggantikan batas konservatif dengan karakterisasi sensitivitas yang akurat dan kalibrasi kebisingan yang mungkin optimal. Pertama, kami menunjukkan bahwa sensitivitas terburuk atas set data berukuran arbitrase dapat ditandai dengan tepat menggunakan hanya dua catatan. Untuk domain ukuran $m$, ini mengurangi analisis ke batas privasi paling besar $m(m-1)$, terlepas dari ukuran dataset. Karakterisasi kami dapat secara arbitrase lebih ketat daripada batas sensitivitas berbasis diameter konvensional, mengungkapkan peningkatan potensial yang tidak ter

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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