# Wavelet Flow For Extragalactic Foreground Simulations

arXiv: https://arxiv.org/abs/2505.21220 · HTML: https://mlsanity.com/paper/2505.21220/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 88 references that are in the map.
- First posted on arXiv 27 May 2025.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Wavelet Flow: Fast Training of High Resolution Normalizing Flows](https://mlsanity.com/paper/2010.13821/) (2020)
- [Translation and Rotation Equivariant Normalizing Flow (TRENF) for Optimal Cosmological Analysis](https://mlsanity.com/paper/2202.05282/) (2022)
- [Multiscale Flow for Robust and Optimal Cosmological Analysis](https://mlsanity.com/paper/2306.04689/) (2023)
- [Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian Deep Learning](https://mlsanity.com/paper/2010.02926/) (2020)
- [Efficient Out-of-Distribution Detection of Melanoma with Wavelet-based Normalizing Flows](https://mlsanity.com/paper/2208.04639/) (2022)

## Built on by (most cited first, 2 of 2)

- [Cosmo3DFlow: Wavelet Flow Matching for Spatial-to-Spectral Compression in Reconstructing the Early Universe](https://mlsanity.com/paper/2602.10172/) (2026)
- [Recovering Weak Signals with Normalizing Flows](https://mlsanity.com/paper/2609.06382/) (2026)

## Abstract (arXiv)

Extragalactic foregrounds in cosmic microwave background (CMB) observations are both a source of cosmological and astrophysical information and a nuisance to the CMB. Effective field-level modeling that captures their non-Gaussian statistical distributions is increasingly important for optimal information extraction, particularly given the precise and low-noise observations from current and upcoming experiments. We explore the use of Wavelet Flow (WF) models to tackle the novel task of modeling the field-level probability distributions of multi-component CMB secondaries and foreground. Specifically, we jointly train correlated CMB lensing convergence (kappa) and cosmic infrared background (CIB) maps with a WF model and obtain a network that statistically recovers the input to high accuracy -- the trained network generates samples of kappa and CIB fields whose average power spectra are within a few percent of the inputs across all scales, and whose Minkowski functionals are similarly accurate compared to the inputs. Leveraging the multiscale architecture of these models, we fine-tune both the model parameters and the priors at each scale independently, optimizing performance across different resolutions. These results demonstrate that WF models can accurately simulate correlated components of CMB secondaries, supporting improved analysis of cosmological data. Our code and trained models can be found here (https://github.com/matiwosm/HybridPriorWavletFlow.git).