# On gradient regularizers for MMD GANs

arXiv: https://arxiv.org/abs/1805.11565 · HTML: https://mlsanity.com/paper/1805.11565/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2018.

## Built on by (most cited first, 28 of 28)

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- [Deep MMD Gradient Flow without adversarial training](https://mlsanity.com/paper/2405.06780/) (2024)
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- [The Geometric Occam's Razor Implicit in Deep Learning](https://mlsanity.com/paper/2111.15090/) (2021)
- [Sobolev Regularized MMD Gradient Flow](https://mlsanity.com/paper/2605.11884/) (2026)
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- [Learning Representations for Independence Testing](https://mlsanity.com/paper/2409.06890/) (2024)
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- [CKGAN: Training Generative Adversarial Networks Using Characteristic Kernel Integral Probability Metrics](https://mlsanity.com/paper/2504.05945/) (2025)
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## Abstract (arXiv)

We propose a principled method for gradient-based regularization of the critic of GAN-like models trained by adversarially optimizing the kernel of a Maximum Mean Discrepancy (MMD). We show that controlling the gradient of the critic is vital to having a sensible loss function, and devise a method to enforce exact, analytical gradient constraints at no additional cost compared to existing approximate techniques based on additive regularizers. The new loss function is provably continuous, and experiments show that it stabilizes and accelerates training, giving image generation models that outperform state-of-the art methods on 160 × 160 CelebA and 64 × 64 unconditional ImageNet.