# Density Deconvolution with Normalizing Flows

arXiv: https://arxiv.org/abs/2006.09396 · HTML: https://mlsanity.com/paper/2006.09396/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve](https://mlsanity.com/paper/2501.08288/) (2025)
- [Neural-g: A Deep Learning Framework for Mixing Density Estimation](https://mlsanity.com/paper/2406.05986/) (2024)
- [Nonparametric Deconvolution and Denoising using Simulation Based Inference](https://mlsanity.com/paper/2606.21907/) (2026)

## Abstract (arXiv)

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but would like to exploit the superior density estimation performance of normalizing flows and allow for arbitrary noise distributions. Since both adjustments lead to an intractable likelihood, we resort to amortized variational inference. We demonstrate some problems involved in this approach, however, experiments on real data demonstrate that flows can already out-perform Gaussian mixtures for density deconvolution.