Diffusion Sensitivity Geometry and Strong Duality for Optimal Privacy-Utility Tradeoffs
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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BibTeX
@misc{do2026diffusion,
title = {{Diffusion Sensitivity Geometry and Strong Duality for Optimal Privacy-Utility Tradeoffs}},
author = {Tue Do and Daniel Alabi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28991},
eprint = {2610.28991},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28991},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diffusion Sensitivity Geometry and Strong Duality for Optimal Privacy-Utility Tradeoffs
AU - Tue Do
AU - Daniel Alabi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28991
UR - https://arxiv.org/abs/2610.28991
AB - 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.
ER -