# InvertibleNetworks.jl: A Julia package for scalable normalizing flows

arXiv: https://arxiv.org/abs/2312.13480 · HTML: https://mlsanity.com/paper/2312.13480/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference](https://mlsanity.com/paper/1905.10687/) (2019)
- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [Preconditioned training of normalizing flows for variational inference in inverse problems](https://mlsanity.com/paper/2101.03709/) (2021)
- [Fully Hyperbolic Convolutional Neural Networks](https://mlsanity.com/paper/1905.10484/) (2019)
- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)
- [Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization](https://mlsanity.com/paper/2004.07871/) (2020)
- [Solving multiphysics-based inverse problems with learned surrogates and constraints](https://mlsanity.com/paper/2307.11099/) (2023)
- [Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantification](https://mlsanity.com/paper/2303.03478/) (2023)
- [Learned multiphysics inversion with differentiable programming and machine learning](https://mlsanity.com/paper/2304.05592/) (2023)
- [Inference of CO2 flow patterns -- a feasibility study](https://mlsanity.com/paper/2311.00290/) (2023)
- [Memory Efficient Invertible Neural Networks for 3D Photoacoustic Imaging](https://mlsanity.com/paper/2204.11850/) (2022)
- [Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics](https://mlsanity.com/paper/2305.08733/) (2023)
- [Symmetric block-low-rank layers for fully reversible multilevel neural networks](https://mlsanity.com/paper/1912.12137/) (2019)

## Built on by (most cited first, 6 of 6)

- [ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problems](https://mlsanity.com/paper/2405.05398/) (2024)
- [Probabilistic Bayesian optimal experimental design using conditional normalizing flows](https://mlsanity.com/paper/2402.18337/) (2024)
- [An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring](https://mlsanity.com/paper/2410.01218/) (2024)
- [Advancing Geological Carbon Storage Monitoring With 3d Digital Shadow Technology](https://mlsanity.com/paper/2502.07169/) (2025)
- [Fully invertible hyperbolic neural networks for segmenting large-scale surface and sub-surface data](https://mlsanity.com/paper/2407.00595/) (2024)
- [Enhancing Robustness Of Digital Shadow For CO2 Storage Monitoring With Augmented Rock Physics Modeling](https://mlsanity.com/paper/2502.07171/) (2025)

## Abstract (arXiv)

InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging the inherent invertibility of normalizing flows, which significantly reduces memory requirements during backpropagation compared to existing normalizing flow packages that rely on automatic differentiation frameworks. InvertibleNetworks.jl has been adapted for diverse applications, including seismic imaging, medical imaging, and CO2 monitoring, demonstrating its effectiveness in learning high-dimensional distributions.