# CINDI: Conditional Imputation and Noisy Data Integrity with Flows in Power Grid Data

arXiv: https://arxiv.org/abs/2603.11745 · HTML: https://mlsanity.com/paper/2603.11745/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Using Trusted Data to Train Deep Networks on Labels Corrupted by Severe Noise](https://mlsanity.com/paper/1802.05300/) (2018)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [SoftPatch: Unsupervised Anomaly Detection with Noisy Data](https://mlsanity.com/paper/2403.14233/) (2024)
- [Distribution-Independent PAC Learning of Halfspaces with Massart Noise](https://mlsanity.com/paper/1906.10075/) (2019)
- [Probabilistic Imputation for Time-series Classification with Missing Data](https://mlsanity.com/paper/2308.06738/) (2023)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [TimeCHEAT: A Channel Harmony Strategy for Irregularly Sampled Multivariate Time Series Analysis](https://mlsanity.com/paper/2412.12886/) (2024)
- [Task-oriented Time Series Imputation Evaluation via Generalized Representers](https://mlsanity.com/paper/2410.06652/) (2024)
- [STING: Self-attention based Time-series Imputation Networks using GAN](https://mlsanity.com/paper/2209.10801/) (2022)
- [Boundary-enhanced time series data imputation with long-term dependency diffusion models](https://mlsanity.com/paper/2501.06585/) (2025)

## Abstract (arXiv)

Real-world multivariate time series, particularly in critical infrastructure such as electrical power grids, are often corrupted by noise and anomalies that degrade the performance of downstream tasks. Standard data cleaning approaches often rely on disjoint strategies, which involve detecting errors with one model and imputing them with another. Such approaches can fail to capture the full joint distribution of the data and ignore prediction uncertainty. This work introduces Conditional Imputation and Noisy Data Integrity (CINDI), an unsupervised probabilistic framework designed to restore data integrity in complex time series. Unlike fragmented approaches, CINDI unifies anomaly detection and imputation into a single end-to-end system built on conditional normalizing flows. By modeling the exact conditional likelihood of the data, the framework identifies low-probability segments and iteratively samples statistically consistent replacements. This allows CINDI to efficiently reuse learned information while preserving the underlying physical and statistical properties of the system. We evaluate the framework using real-world grid loss data from a Norwegian power distribution operator, though the methodology is designed to generalize to any multivariate time series domain. The results demonstrate that CINDI yields robust performance compared to competitive baselines, offering a scalable solution for maintaining reliability in noisy environments.