# Recovering Weak Signals with Normalizing Flows

arXiv: https://arxiv.org/abs/2609.06382 · HTML: https://mlsanity.com/paper/2609.06382/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 6 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [Noise Flow: Noise Modeling with Conditional Normalizing Flows](https://mlsanity.com/paper/1908.08453/) (2019)
- [Deep Unfolding with Normalizing Flow Priors for Inverse Problems](https://mlsanity.com/paper/2107.02848/) (2021)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [Canonical normalizing flows for manifold learning](https://mlsanity.com/paper/2310.12743/) (2023)
- [Distributed Radio Interferometric Calibration](https://mlsanity.com/paper/1502.00858/) (2015)
- [mathttemuflow: Normalising Flows for Joint Cosmological Analysis](https://mlsanity.com/paper/2409.01407/) (2024)
- [Contrastive Normalizing Flows for Uncertainty-Aware Parameter Estimation](https://mlsanity.com/paper/2505.08709/) (2025)
- [Wavelet Flow For Extragalactic Foreground Simulations](https://mlsanity.com/paper/2505.21220/) (2025)
- [Profiling systematic uncertainties in Simulation-Based Inference with Factorizable Normalizing Flows](https://mlsanity.com/paper/2602.13184/) (2026)
- [Performance Analysis of Distributed Radio Interferometric Calibration](https://mlsanity.com/paper/1805.00265/) (2018)

## Abstract (arXiv)

In many scientific disciplines, weak signals of interest are obscured by dominant nuisance signals that are several orders of magnitude stronger. Recovering these weak signals requires subtracting the dominant ones; however, this calibration process inherently distorts or partially suppresses the underlying signal of interest. To address this problem, we propose the use of normalizing flow models to reconstruct calibration-affected weak signals. By leveraging the statistical invariance of the target signals and assuming minimal initial suppression, our framework effectively recovers the lost signal components. We provide a comprehensive theoretical overview of this normalizing flow-based recovery method and demonstrate its efficacy using simulated data.