Energy Time-Series Imputation with Differentially Private Diffusion Models via Clipping-Aware Objective Conditioning

A new arXiv paper (arXiv:2610.00209v1) proposes clipping-aware objective conditioning to improve differentially private diffusion models for energy time-series imputation, using v-prediction instead of standard ε-prediction to reduce large pre-clipping gradients at late low-SNR timesteps under cosine diffusion schedules. Evaluated on five real-world energy time-series datasets across random point missingness, contiguous block missingness, persistent outages, and multiple missing-data severities, the method consistently improved imputation utility over the ε-prediction baseline under matched DP-SGD settings. Gradient diagnostics showed lower upper-tail pre-clipping gradient norms, reduced clipping fractions, and stronger attenuation at late low-SNR timesteps.

arXiv:2610.00209v1 Announce Type: new Abstract: Reliable recovery of missing measurements is important for monitoring and analysis in energy time-series systems, where fine-grained measurements may contain sensitive temporal information. Diffusion models trained with differentially private stochastic gradient descent DP-SGD provide a promising framework for privacy-sensitive energy time-series imputation. Under cosine diffusion schedules, late timesteps correspond to low signal-to-noise ratio SNR conditions, where standard $\varepsilon$-prediction can induce large pre-clipping gradients. Such gradients are more likely to be clipped, reducing the retained optimization signal. The artificial intelligence AI contribution lies in formulating this objective--clipping interaction as an objective optimization problem under fixed-threshold DP-SGD and developing timestep-aware objective conditioning for diffusion-based energy time-series imputation. The method adopts $v$-prediction to mitigate late-timestep gradient amplification, uses static loss weighting as a uniform-scaling control, and introduces diffusion-schedule-aware dynamic weighting for stronger attenuation before clipping. For the engineering application, we evaluate the method on five real-world energy time-series datasets across random point missingness, contiguous block missingness, persistent outages, and multiple missing-data severities. Under matched DP-SGD settings, the proposed method consistently improves imputation utility over the $\varepsilon$-prediction baseline. Gradient diagnostics reveal lower upper-tail pre-clipping gradient norms, reduced clipping fractions, and stronger attenuation at late low-SNR timesteps, supporting the effectiveness of clipping-aware objective conditioning for energy time-series imputation.