# Detection and Imputation based Two-Stage Denoising Diffusion Power System Measurement Recovery under Cyber-Physical Uncertainties

arXiv: https://arxiv.org/abs/2312.04346 · HTML: https://mlsanity.com/paper/2312.04346/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Fast ODE-based Sampling for Diffusion Models in Around 5 Steps](https://mlsanity.com/paper/2312.00094/) (2023)
- [The Creation and Validation of Load Time Series for Synthetic Electric Power Systems](https://mlsanity.com/paper/1911.06934/) (2019)
- [Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter with Enhanced Numerical Stability](https://mlsanity.com/paper/1509.07394/) (2015)
- [Risk Mitigation for Dynamic State Estimation Against Cyber Attacks and Unknown Inputs](https://mlsanity.com/paper/1508.07246/) (2015)
- [False Data Injection Attacks and the Distributed Countermeasure in DC Microgrids](https://mlsanity.com/paper/2001.01984/) (2020)
- [Enhancing Cyber-Resiliency of DER-based SmartGrid: A Survey](https://mlsanity.com/paper/2305.05338/) (2023)

## Built on by (most cited first, 5 of 5)

- [Deep Learning Advancements in Anomaly Detection: A Comprehensive Survey](https://mlsanity.com/paper/2503.13195/) (2025)
- [Latent Diffusion Model-Enabled Low-Latency Semantic Communication in the Presence of Semantic Ambiguities and Wireless Channel Noises](https://mlsanity.com/paper/2406.06644/) (2024)
- [Generalized Multi-Objective Reinforcement Learning with Envelope Updates in URLLC-enabled Vehicular Networks](https://mlsanity.com/paper/2405.11331/) (2024)
- [TOAST: Task-Oriented Adaptive Semantic Transmission over Dynamic Wireless Environments](https://mlsanity.com/paper/2506.21900/) (2025)
- [EMFusion: Uncertainty-Aware Conditional Diffusion Model for Multivariate Narrow-band Exposure Forecasting](https://mlsanity.com/paper/2512.15067/) (2025)

## Abstract (arXiv)

Power system cyber-physical uncertainties, including measurement ambiguities stemming from cyber attacks and data losses, along with system uncertainties introduced by massive renewables and complex dynamics, reduce the likelihood of enhancing the quality of measurements. Fortunately, denoising diffusion models exhibit powerful learning and generation abilities for the complex underlying physics of the real world. To this end, this paper proposes an improved detection and imputation based two-stage denoising diffusion model (TSDM) to identify and reconstruct the measurements with various cyber-physical uncertainties. The first stage of the model comprises a classifier-guided conditional anomaly detection component, while the second stage involves diffusion-based measurement imputation component. Moreover, the proposed TSDM adopts optimal variance to accelerate the diffusion generation process with subsequence sampling. Extensive numerical case studies demonstrate that the proposed TSDM can accurately recover power system measurements despite renewables-induced strong randomness and highly nonlinear dynamics. Additionally, the proposed TSDM has stronger robustness compared to existing reconstruction networks and exhibits lower computational complexity than general denoising diffusion models.