Papers › Sliced Iterative Normalizing Flows

Sliced Iterative Normalizing Flows

1 Jul 2020ICML Workshop INNF 2021 7arXiv:2007.00674archive 2025-07-28

Biwei Dai, Uros Seljak

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.

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Syntology Ran 1 of 4 code samples harvested from 1 repository linked to this paper; 3 have no recorded run. Of those that ran: 1 ran · our draft was wrong.

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biweidai/SIG officialmentioned on GitHubpytorch report
biweidai/SINF mentioned on GitHubpytorch report

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1ran · our draft was wrong
3unverified

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toimage biweidai/SINF/sinf/SIG.py community (archive-listed) ran · our draft was wrong no licence file found · pointer only · 317038bbf1e9dea6 · report
GIS biweidai/SINF/sinf/GIS.py community (archive-listed) unverified no licence file found · pointer only · 79dc956417fc1b4c · report
add_one_layer_inverse biweidai/SINF/sinf/SIG.py community (archive-listed) unverified no licence file found · pointer only · d0297731c19c4d45 · report
preprocess biweidai/SINF/sinf/SIG.py community (archive-listed) unverified no licence file found · pointer only · e9d36e5bf9c963a2 · report

Tasks

Density EstimationImage GenerationOut-of-Distribution Detection

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Image Generation Fashion-MNIST Sliced Iterative Generator FID 13.7 #2 of 7 Archive leaderboard report
Image Generation MNIST Sliced Iterative Generator FID 4.5 #6 of 15 Archive leaderboard report
Image Generation MNIST Sliced Iterative Generator bits/dimension 1.34 #6 of 15 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

Normalizing FlowsSIG

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