# Sliced Iterative Normalizing Flows

arXiv: https://arxiv.org/abs/2007.00674 · HTML: https://mlsanity.com/paper/2007.00674/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 30 of 38)

- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [Generative Sliced MMD Flows with Riesz Kernels](https://mlsanity.com/paper/2305.11463/) (2023)
- [Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections](https://mlsanity.com/paper/2106.15427/) (2021)
- [Sampling in Unit Time with Kernel Fisher-Rao Flow](https://mlsanity.com/paper/2401.03892/) (2024)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Hierarchical Sliced Wasserstein Distance](https://mlsanity.com/paper/2209.13570/) (2022)
- [Efficient Gradient Flows in Sliced-Wasserstein Space](https://mlsanity.com/paper/2110.10972/) (2021)
- [Amortized Projection Optimization for Sliced Wasserstein Generative Models](https://mlsanity.com/paper/2203.13417/) (2022)
- [Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flows](https://mlsanity.com/paper/2305.02164/) (2023)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inference](https://mlsanity.com/paper/2205.14240/) (2022)
- [Neural Sinkhorn Gradient Flow](https://mlsanity.com/paper/2401.14069/) (2024)
- [Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimation](https://mlsanity.com/paper/2308.01054/) (2023)
- [Measure transfer via stochastic slicing and matching](https://mlsanity.com/paper/2307.05705/) (2023)
- [On the Convergence Rate of Gaussianization with Random Rotations](https://mlsanity.com/paper/2306.13520/) (2023)
- [Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models](https://mlsanity.com/paper/2407.04958/) (2024)
- [Iterative Alignment Flows](https://mlsanity.com/paper/2104.07232/) (2021)
- [Cooperative Distribution Alignment via JSD Upper Bound](https://mlsanity.com/paper/2207.02286/) (2022)
- [Iterative Flow Matching: Path Correction and Gradual Refinement for Enhanced Generative Modeling](https://mlsanity.com/paper/2502.16445/) (2025)
- [Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis](https://mlsanity.com/paper/2502.06525/) (2025)
- [Flow Annealed Kalman Inversion for Gradient-Free Inference in Bayesian Inverse Problems](https://mlsanity.com/paper/2309.11490/) (2023)
- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [Convergence Rates for Distribution Matching with Sliced Optimal Transport](https://mlsanity.com/paper/2602.10691/) (2026)
- [Trust the Critics: Generatorless and Multipurpose WGANs with Initial Convergence Guarantees](https://mlsanity.com/paper/2111.15099/) (2021)
- [Fast Approximation of the Generalized Sliced-Wasserstein Distance](https://mlsanity.com/paper/2210.10268/) (2022)
- [ShuffleFlow: Scalable Posterior Inference for Bayesian Inverse Imaging](https://mlsanity.com/paper/2606.21099/) (2026)
- [One-Sided Quantile Coupling for Flow Matching](https://mlsanity.com/paper/2608.00978/) (2026)
- [Efficient CDF Approximations for Normalizing Flows](https://mlsanity.com/paper/2202.11322/) (2022)
- [Kernelised Normalising Flows](https://mlsanity.com/paper/2307.14839/) (2023)

## Abstract (arXiv)

We develop an iterative (greedy) deep learning (DL) algorithm which is able to transform an arbitrary probability distribution function (PDF) into the target PDF. The model is based on iterative Optimal Transport of a series of 1D slices, matching on each slice the marginal PDF to the target. The axes of the orthogonal slices are chosen to maximize the PDF difference using Wasserstein distance at each iteration, which enables the algorithm to scale well to high dimensions. As special cases of this algorithm, we introduce two sliced iterative Normalizing Flow (SINF) models, which map from the data to the latent space (GIS) and vice versa (SIG). We show that SIG is able to generate high quality samples of image datasets, which match the GAN benchmarks, while GIS obtains competitive results on density estimation tasks compared to the density trained NFs, and is more stable, faster, and achieves higher p(x) when trained on small training sets. SINF approach deviates significantly from the current DL paradigm, as it is greedy and does not use concepts such as mini-batching, stochastic gradient descent and gradient back-propagation through deep layers.