# Demystifying MMD GANs

arXiv: https://arxiv.org/abs/1801.01401 · HTML: https://mlsanity.com/paper/1801.01401/

## Key facts

- Cited by 1,293 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2018.

## Built on by (most cited first, 30 of 1293)

- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Multi-Concept Customization of Text-to-Image Diffusion](https://mlsanity.com/paper/2212.04488/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Habitat-Matterport 3D Dataset (HM3D): 1000 Large-scale 3D Environments for Embodied AI](https://mlsanity.com/paper/2109.08238/) (2021)
- [StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis](https://mlsanity.com/paper/2110.08985/) (2021)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [ELITE: Encoding Visual Concepts into Textual Embeddings for Customized Text-to-Image Generation](https://mlsanity.com/paper/2302.13848/) (2023)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [StyleSDF: High-Resolution 3D-Consistent Image and Geometry Generation](https://mlsanity.com/paper/2112.11427/) (2021)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Generative Novel View Synthesis with 3D-Aware Diffusion Models](https://mlsanity.com/paper/2304.02602/) (2023)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Transformers in Medical Imaging: A Survey](https://mlsanity.com/paper/2201.09873/) (2022)
- [Text2Tex: Text-driven Texture Synthesis via Diffusion Models](https://mlsanity.com/paper/2303.11396/) (2023)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Large Scale Image Completion via Co-Modulated Generative Adversarial Networks](https://mlsanity.com/paper/2103.10428/) (2021)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [GRAM: Generative Radiance Manifolds for 3D-Aware Image Generation](https://mlsanity.com/paper/2112.08867/) (2021)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Projected GANs Converge Faster](https://mlsanity.com/paper/2111.01007/) (2021)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [DiffRF: Rendering-Guided 3D Radiance Field Diffusion](https://mlsanity.com/paper/2212.01206/) (2022)
- [BrushNet: A Plug-and-Play Image Inpainting Model with Decomposed Dual-Branch Diffusion](https://mlsanity.com/paper/2403.06976/) (2024)

## Abstract (arXiv)

We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss functions raised by recent work: we show that gradient estimators used in the optimization process for both MMD GANs and Wasserstein GANs are unbiased, but learning a discriminator based on samples leads to biased gradients for the generator parameters. We also discuss the issue of kernel choice for the MMD critic, and characterize the kernel corresponding to the energy distance used for the Cramer GAN critic. Being an integral probability metric, the MMD benefits from training strategies recently developed for Wasserstein GANs. In experiments, the MMD GAN is able to employ a smaller critic network than the Wasserstein GAN, resulting in a simpler and faster-training algorithm with matching performance. We also propose an improved measure of GAN convergence, the Kernel Inception Distance, and show how to use it to dynamically adapt learning rates during GAN training.