# In the light of feature distributions: moment matching for Neural Style Transfer

arXiv: https://arxiv.org/abs/2103.07208 · HTML: https://mlsanity.com/paper/2103.07208/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Universal Style Transfer via Feature Transforms](https://mlsanity.com/paper/1705.08086/) (2017)
- [A Learned Representation For Artistic Style](https://mlsanity.com/paper/1610.07629/) (2016)
- [Unsupervised Pixel-Level Domain Adaptation with Generative Adversarial Networks](https://mlsanity.com/paper/1612.05424/) (2016)
- [Neural Style Transfer: A Review](https://mlsanity.com/paper/1705.04058/) (2017)
- [Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learning](https://mlsanity.com/paper/1702.08811/) (2017)
- [Texture Networks: Feed-forward Synthesis of Textures and Stylized Images](https://mlsanity.com/paper/1603.03417/) (2016)
- [Style Transfer by Relaxed Optimal Transport and Self-Similarity](https://mlsanity.com/paper/1904.12785/) (2019)
- [Demystifying Neural Style Transfer](https://mlsanity.com/paper/1701.01036/) (2017)
- [The Contextual Loss for Image Transformation with Non-Aligned Data](https://mlsanity.com/paper/1803.02077/) (2018)
- [Domain Adaptation for Visual Applications: A Comprehensive Survey](https://mlsanity.com/paper/1702.05374/) (2017)
- [Combining Markov Random Fields and Convolutional Neural Networks for Image Synthesis](https://mlsanity.com/paper/1601.04589/) (2016)
- [Controlling Perceptual Factors in Neural Style Transfer](https://mlsanity.com/paper/1611.07865/) (2016)
- [Fast Patch-based Style Transfer of Arbitrary Style](https://mlsanity.com/paper/1612.04337/) (2016)
- [Deep Visual Domain Adaptation](https://mlsanity.com/paper/2012.14176/) (2020)
- [Stable and Controllable Neural Texture Synthesis and Style Transfer Using Histogram Losses](https://mlsanity.com/paper/1701.08893/) (2017)
- [Diversified Texture Synthesis with Feed-forward Networks](https://mlsanity.com/paper/1703.01664/) (2017)
- [A Closed-form Solution to Universal Style Transfer](https://mlsanity.com/paper/1906.00668/) (2019)
- [Robust Unsupervised Domain Adaptation for Neural Networks via Moment Alignment](https://mlsanity.com/paper/1711.06114/) (2017)
- [Wasserstein Style Transfer](https://mlsanity.com/paper/1905.12828/) (2019)
- [Laplacian-Steered Neural Style Transfer](https://mlsanity.com/paper/1707.01253/) (2017)

## Built on by (most cited first, 26 of 26)

- [Exact Feature Distribution Matching for Arbitrary Style Transfer and Domain Generalization](https://mlsanity.com/paper/2203.07740/) (2022)
- [StyleMesh: Style Transfer for Indoor 3D Scene Reconstructions](https://mlsanity.com/paper/2112.01530/) (2021)
- [Learning Graph Neural Networks for Image Style Transfer](https://mlsanity.com/paper/2207.11681/) (2022)
- [DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices](https://mlsanity.com/paper/2303.13325/) (2023)
- [A Coreset Selection of Coreset Selection Literature: Introduction and Recent Advances](https://mlsanity.com/paper/2505.17799/) (2025)
- [Generalized One-shot Domain Adaptation of Generative Adversarial Networks](https://mlsanity.com/paper/2209.03665/) (2022)
- [All-to-key Attention for Arbitrary Style Transfer](https://mlsanity.com/paper/2212.04105/) (2022)
- [Transforming Radiance Field with Lipschitz Network for Photorealistic 3D Scene Stylization](https://mlsanity.com/paper/2303.13232/) (2023)
- [Learning Dynamic Style Kernels for Artistic Style Transfer](https://mlsanity.com/paper/2304.00414/) (2023)
- [Artwork Protection Against Neural Style Transfer Using Locally Adaptive Adversarial Color Attack](https://mlsanity.com/paper/2401.09673/) (2024)
- [Temporal Context Matters: Enhancing Single Image Prediction with Disease Progression Representations](https://mlsanity.com/paper/2203.01933/) (2022)
- [Continual Unsupervised Domain Adaptation for Semantic Segmentation using a Class-Specific Transfer](https://mlsanity.com/paper/2208.06507/) (2022)
- [NaturalInversion: Data-Free Image Synthesis Improving Real-World Consistency](https://mlsanity.com/paper/2306.16661/) (2023)
- [StyO: Stylize Your Face in Only One-shot](https://mlsanity.com/paper/2303.03231/) (2023)
- [Interactive Image Manipulation with Complex Text Instructions](https://mlsanity.com/paper/2211.15352/) (2022)
- [SCSA: A Plug-and-Play Semantic Continuous-Sparse Attention for Arbitrary Semantic Style Transfer](https://mlsanity.com/paper/2503.04119/) (2025)
- [ALADIN-NST: Self-supervised disentangled representation learning of artistic style through Neural Style Transfer](https://mlsanity.com/paper/2304.05755/) (2023)
- [FaceRefiner: High-Fidelity Facial Texture Refinement with Differentiable Rendering-based Style Transfer](https://mlsanity.com/paper/2601.04520/) (2026)
- [TSSAT: Two-Stage Statistics-Aware Transformation for Artistic Style Transfer](https://mlsanity.com/paper/2309.06004/) (2023)
- [Geometric Moment Alignment for Domain Adaptation via Siegel Embeddings](https://mlsanity.com/paper/2510.14666/) (2025)
- [BiasBed -- Rigorous Texture Bias Evaluation](https://mlsanity.com/paper/2211.13190/) (2022)
- [LaCoOT: Layer Collapse through Optimal Transport](https://mlsanity.com/paper/2406.08933/) (2024)
- [Leveraging Diffusion Models for Stylization using Multiple Style Images](https://mlsanity.com/paper/2508.12784/) (2025)
- [Non-Parametric Style Transfer](https://mlsanity.com/paper/2206.12921/) (2022)
- [Is Generative Modeling-based Stylization Necessary for Domain Adaptation in Regression Tasks?](https://mlsanity.com/paper/2306.01706/) (2023)
- [AEANet: Affinity Enhanced Attentional Networks for Arbitrary Style Transfer](https://mlsanity.com/paper/2409.14652/) (2024)

## Abstract (arXiv)

Style transfer aims to render the content of a given image in the graphical/artistic style of another image. The fundamental concept underlying NeuralStyle Transfer (NST) is to interpret style as a distribution in the feature space of a Convolutional Neural Network, such that a desired style can be achieved by matching its feature distribution. We show that most current implementations of that concept have important theoretical and practical limitations, as they only partially align the feature distributions. We propose a novel approach that matches the distributions more precisely, thus reproducing the desired style more faithfully, while still being computationally efficient. Specifically, we adapt the dual form of Central Moment Discrepancy (CMD), as recently proposed for domain adaptation, to minimize the difference between the target style and the feature distribution of the output image. The dual interpretation of this metric explicitly matches all higher-order centralized moments and is therefore a natural extension of existing NST methods that only take into account the first and second moments. Our experiments confirm that the strong theoretical properties also translate to visually better style transfer, and better disentangle style from semantic image content.