Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal dynamics, and therefore can assign high probability to anomalous or out-of-distribution samples. We address this structural limitation by relocating the notion of anomaly to a prescribed latent space. We introduce explicit inductive biases in conditional normalizing flows, modeling time-series observations within a discrete-time state-space framework that constrains latent representations to evolve according to prescribed temporal dynamics. Under this formulation, expected behavior corresponds to compliance with a specified distribution over latent trajectories, while anomalies are defined as violations of these dynamics. Anomaly detection is consequently reduced to a statistically grounded compliance test, such that observations are mapped to latent space and evaluated via goodness-of-fit tests against the prescribed latent evolution. This yields a principled decision rule that remains effective even in regions of high observation likelihood. Experiments on synthetic and real-world time-series demonstrate reliable detection of anomalies in frequency, amplitude, and observation noise, while providing interpretable diagnostics of model compliance.

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

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.

Temporal-Conditioned Normalizing Flows for Multivariate Time Series Anomaly Detection

This paper introduces temporal-conditioned normalizing flows (tcNF), a novel framework that addresses anomaly detection in time series data with accurate modeling of temporal dependencies and uncertainty. By conditioning normalizing flows on previous observations, tcNF effectively captures complex temporal dynamics and generates accurate probability distributions of expected behavior. This autoregressive approach enables robust anomaly detection by identifying low-probability events within the learned distribution. We evaluate tcNF on diverse datasets, demonstrating good accuracy and robustness compared to existing methods. A comprehensive analysis of strengths and limitations and open-source code is provided to facilitate reproducibility and future research.