# Gaussianization Flows

arXiv: https://arxiv.org/abs/2003.01941 · HTML: https://mlsanity.com/paper/2003.01941/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 20 of 20)

- [Concrete Score Matching: Generalized Score Matching for Discrete Data](https://mlsanity.com/paper/2211.00802/) (2022)
- [Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flows](https://mlsanity.com/paper/2305.02164/) (2023)
- [Jacobian Determinant of Normalizing Flows](https://mlsanity.com/paper/2102.06539/) (2021)
- [Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation](https://mlsanity.com/paper/2106.10591/) (2021)
- [Whitening Convergence Rate of Coupling-based Normalizing Flows](https://mlsanity.com/paper/2210.14032/) (2022)
- [Normalizing Flows for Knockoff-free Controlled Feature Selection](https://mlsanity.com/paper/2106.01528/) (2021)
- [On the Convergence Rate of Gaussianization with Random Rotations](https://mlsanity.com/paper/2306.13520/) (2023)
- [Iterative Flow Matching: Path Correction and Gradual Refinement for Enhanced Generative Modeling](https://mlsanity.com/paper/2502.16445/) (2025)
- [Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models](https://mlsanity.com/paper/2112.03860/) (2021)
- [Orthonormal Convolutions for the Rotation Based Iterative Gaussianization](https://mlsanity.com/paper/2206.03860/) (2022)
- [TERM Model: Tensor Ring Mixture Model for Density Estimation](https://mlsanity.com/paper/2312.08075/) (2023)
- [Rotated Mean-Field Variational Inference and Iterative Gaussianization](https://mlsanity.com/paper/2510.07732/) (2025)
- [Analytic Bijections for Smooth and Interpretable Normalizing Flows](https://mlsanity.com/paper/2601.10774/) (2026)
- [ShuffleFlow: Scalable Posterior Inference for Bayesian Inverse Imaging](https://mlsanity.com/paper/2606.21099/) (2026)
- [Neural PCA for Flow-Based Representation Learning](https://mlsanity.com/paper/2208.10753/) (2022)
- [Kernelised Normalising Flows](https://mlsanity.com/paper/2307.14839/) (2023)
- [MixerFlow: MLP-Mixer meets Normalising Flows](https://mlsanity.com/paper/2310.16777/) (2023)
- [NF-SLAM: Effective, Normalizing Flow-supported Neural Field representations for object-level visual SLAM in automotive applications](https://mlsanity.com/paper/2503.11199/) (2025)
- [Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis](https://mlsanity.com/paper/2507.11192/) (2025)
- [Generative Nested Sampling of Atomistic Thermodynamic Landscapes](https://mlsanity.com/paper/2609.03193/) (2026)

## Abstract (arXiv)

Iterative Gaussianization is a fixed-point iteration procedure that can transform any continuous random vector into a Gaussian one. Based on iterative Gaussianization, we propose a new type of normalizing flow model that enables both efficient computation of likelihoods and efficient inversion for sample generation. We demonstrate that these models, named Gaussianization flows, are universal approximators for continuous probability distributions under some regularity conditions. Because of this guaranteed expressivity, they can capture multimodal target distributions without compromising the efficiency of sample generation. Experimentally, we show that Gaussianization flows achieve better or comparable performance on several tabular datasets compared to other efficiently invertible flow models such as Real NVP, Glow and FFJORD. In particular, Gaussianization flows are easier to initialize, demonstrate better robustness with respect to different transformations of the training data, and generalize better on small training sets.