# Semi-Supervised Learning with Normalizing Flows

arXiv: https://arxiv.org/abs/1912.13025 · HTML: https://mlsanity.com/paper/1912.13025/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2019.

## Built on by (most cited first, 30 of 76)

- [GMMSeg: Gaussian Mixture based Generative Semantic Segmentation Models](https://mlsanity.com/paper/2210.02025/) (2022)
- [DOC2PPT: Automatic Presentation Slides Generation from Scientific Documents](https://mlsanity.com/paper/2101.11796/) (2021)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [Normalizing Flows for Human Pose Anomaly Detection](https://mlsanity.com/paper/2211.10946/) (2022)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Universal approximation property of invertible neural networks](https://mlsanity.com/paper/2204.07415/) (2022)
- [ECINN: Efficient Counterfactuals from Invertible Neural Networks](https://mlsanity.com/paper/2103.13701/) (2021)
- [Constructing Balance from Imbalance for Long-tailed Image Recognition](https://mlsanity.com/paper/2208.02567/) (2022)
- [Detecting Multivariate Time Series Anomalies with Zero Known Label](https://mlsanity.com/paper/2208.02108/) (2022)
- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)
- [On Training Sample Memorization: Lessons from Benchmarking Generative Modeling with a Large-scale Competition](https://mlsanity.com/paper/2106.03062/) (2021)
- [Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model](https://mlsanity.com/paper/2209.08739/) (2022)
- [Chroma-VAE: Mitigating Shortcut Learning with Generative Classifiers](https://mlsanity.com/paper/2211.15231/) (2022)
- [Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstruction](https://mlsanity.com/paper/2106.03135/) (2021)
- [Task-agnostic Continual Learning with Hybrid Probabilistic Models](https://mlsanity.com/paper/2106.12772/) (2021)
- [On the expressivity of bi-Lipschitz normalizing flows](https://mlsanity.com/paper/2107.07232/) (2021)
- [Towards the Uncharted: Density-Descending Feature Perturbation for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2403.06462/) (2024)
- [PreGenie: An Agentic Framework for High-quality Visual Presentation Generation](https://mlsanity.com/paper/2505.21660/) (2025)
- [Label-Free Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2312.11549/) (2023)
- [A Review of Change of Variable Formulas for Generative Modeling](https://mlsanity.com/paper/2308.02652/) (2023)
- [LiftPool: Bidirectional ConvNet Pooling](https://mlsanity.com/paper/2104.00996/) (2021)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)
- [Differentially Private Normalizing Flows for Privacy-Preserving Density Estimation](https://mlsanity.com/paper/2103.14068/) (2021)
- [Towards Accurate Open-Set Recognition via Background-Class Regularization](https://mlsanity.com/paper/2207.10287/) (2022)
- [Designing a Conditional Prior Distribution for Flow-Based Generative Models](https://mlsanity.com/paper/2502.09611/) (2025)
- [CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flows](https://mlsanity.com/paper/2303.14668/) (2023)
- [Class-Imbalanced Complementary-Label Learning via Weighted Loss](https://mlsanity.com/paper/2209.14189/) (2022)
- [Normalizing flow sampling with Langevin dynamics in the latent space](https://mlsanity.com/paper/2305.12149/) (2023)
- [Improving VAE-based Representation Learning](https://mlsanity.com/paper/2205.14539/) (2022)
- [Coupled Variational Autoencoder](https://mlsanity.com/paper/2306.02565/) (2023)

## Abstract (arXiv)

Normalizing flows transform a latent distribution through an invertible neural network for a flexible and pleasingly simple approach to generative modelling, while preserving an exact likelihood. We propose FlowGMM, an end-to-end approach to generative semi supervised learning with normalizing flows, using a latent Gaussian mixture model. FlowGMM is distinct in its simplicity, unified treatment of labelled and unlabelled data with an exact likelihood, interpretability, and broad applicability beyond image data. We show promising results on a wide range of applications, including AG-News and Yahoo Answers text data, tabular data, and semi-supervised image classification. We also show that FlowGMM can discover interpretable structure, provide real-time optimization-free feature visualizations, and specify well calibrated predictive distributions.