Privacy concerns have led to a surge in the creation of synthetic datasets,
with diffusion models emerging as a promising avenue. Although prior studies
have performed empirical evaluations on these models, there has been a gap in
providing a mathematical characterization of their privacy-preserving
capabilities. To address this, we present the pioneering theoretical
exploration of the privacy preservation inherent in discrete diffusion models
(DDMs) for discrete dataset generation. Focusing on per-instance differential
privacy (pDP), our framework elucidates the potential privacy leakage for each
data point in a given training dataset, offering insights into data
preprocessing to reduce privacy risks of the synthetic dataset generation via
DDMs. Our bounds also show that training with $s$-sized data points leads to a
surge in privacy leakage from $(\epsilon,
\mathcal{O}(\frac{1}{s^2\epsilon}))$-pDP to $(\epsilon,
\mathcal{O}(\frac{1}{s\epsilon}))$-pDP during the transition from the pure
noise to the synthetic clean data phase, and a faster decay in diffusion
coefficients amplifies the privacy guarantee. Finally, we empirically verify
our theoretical findings on both synthetic and real-world datasets.

基于离散扩散模型的数据生成方法的隐私保护能力在理论上进行了开拓性研究，重点研究了每个数据点的潜在隐私泄露，并通过数据预处理减少离散扩散模型生成的合成数据的隐私风险。同时，实验证实了理论研究结果对合成数据和真实世界数据的适用性。