# Manifold Matching via Deep Metric Learning for Generative Modeling

arXiv: https://arxiv.org/abs/2106.10777 · HTML: https://mlsanity.com/paper/2106.10777/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 57 references that are in the map.
- First posted on arXiv 20 Jun 2021.

## Builds on (most cited first, 30 of 30)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [Toward Real-World Single Image Super-Resolution: A New Benchmark and A New Model](https://mlsanity.com/paper/1904.00523/) (2019)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [The relativistic discriminator: a key element missing from standard GAN](https://mlsanity.com/paper/1807.00734/) (2018)
- [Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1903.04064/) (2019)
- [Geometric GAN](https://mlsanity.com/paper/1705.02894/) (2017)
- [EnhanceNet: Single Image Super-Resolution Through Automated Texture Synthesis](https://mlsanity.com/paper/1612.07919/) (2016)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Structure-Preserving Super Resolution with Gradient Guidance](https://mlsanity.com/paper/2003.13081/) (2020)
- [Image GANs meet Differentiable Rendering for Inverse Graphics and Interpretable 3D Neural Rendering](https://mlsanity.com/paper/2010.09125/) (2020)
- [RL-CycleGAN: Reinforcement Learning Aware Simulation-To-Real](https://mlsanity.com/paper/2006.09001/) (2020)
- [Closed-loop Matters: Dual Regression Networks for Single Image Super-Resolution](https://mlsanity.com/paper/2003.07018/) (2020)
- [Variational Autoencoders Pursue PCA Directions (by Accident)](https://mlsanity.com/paper/1812.06775/) (2018)
- [Deep Burst Super-Resolution](https://mlsanity.com/paper/2101.10997/) (2021)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Sliced Wasserstein Generative Models](https://mlsanity.com/paper/1904.05408/) (2019)
- [Guided Variational Autoencoder for Disentanglement Learning](https://mlsanity.com/paper/2004.01255/) (2020)
- [Natural and Realistic Single Image Super-Resolution with Explicit Natural Manifold Discrimination](https://mlsanity.com/paper/1911.03624/) (2019)
- [A Geometric View of Optimal Transportation and Generative Model](https://mlsanity.com/paper/1710.05488/) (2017)
- [Manifold Matching using Shortest-Path Distance and Joint Neighborhood Selection](https://mlsanity.com/paper/1412.4098/) (2014)

## Built on by (most cited first, 3 of 3)

- [Adaptive Feature Interpolation for Low-Shot Image Generation](https://mlsanity.com/paper/2112.02450/) (2021)
- [Geometric Decoupling: Diagnosing the Structural Instability of Latent](https://mlsanity.com/paper/2604.18804/) (2026)
- [Your Data Manifold is Secretly a Reward Model: Shell-LCC for Text-to-Video Generation](https://mlsanity.com/paper/2606.30248/) (2026)

## Abstract (arXiv)

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional Euclidean space. The distribution generator aims at generating samples that follow some distribution condensed around the real data manifold. It is achieved by matching two sets of points using their geometric shape descriptors, such as centroid and p-diameter, with learned distance metric; the metric generator utilizes both real data and generated samples to learn a distance metric which is close to some intrinsic geodesic distance on the real data manifold. The produced distance metric is further used for manifold matching. The two networks are learned simultaneously during the training process. We apply the approach on both unsupervised and supervised learning tasks: in unconditional image generation task, the proposed method obtains competitive results compared with existing generative models; in super-resolution task, we incorporate the framework in perception-based models and improve visual qualities by producing samples with more natural textures. Experiments and analysis demonstrate the feasibility and effectiveness of the proposed framework.