Papers › SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layer
SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layer
Yuhta Takida, Masaaki Imaizumi, Takashi Shibuya, Chieh-Hsin Lai, Toshimitsu Uesaka, Naoki Murata, Yuki Mitsufuji
Generative adversarial networks (GANs) learn a target probability distribution by optimizing a generator and a discriminator with minimax objectives. This paper addresses the question of whether such optimization actually provides the generator with gradients that make its distribution close to the target distribution. We derive metrizable conditions, sufficient conditions for the discriminator to serve as the distance between the distributions by connecting the GAN formulation with the concept of sliced optimal transport. Furthermore, by leveraging these theoretical results, we propose a novel GAN training scheme, called slicing adversarial network (SAN). With only simple modifications, a broad class of existing GANs can be converted to SANs. Experiments on synthetic and image datasets support our theoretical results and the SAN's effectiveness as compared to usual GANs. Furthermore, we also apply SAN to StyleGAN-XL, which leads to state-of-the-art FID score amongst GANs for class conditional generation on ImageNet 256×256. Our implementation is available on https://ytakida.github.io/san.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Generation | CIFAR-10 | StyleSAN-XL | FID | 1.36 | #3 of 78 | Archive leaderboard | report |
| Image Generation | FFHQ 1024 x 1024 | StyleSAN-XL | FID | 1.61 | #1 of 20 | Archive leaderboard | report |
| Image Generation | FFHQ 256 x 256 | StyleSAN-XL | FID | 1.68 | #1 of 51 | Archive leaderboard | report |
| Image Generation | FFHQ 512 x 512 | StyleSAN-XL | FID | 1.77 | #1 of 3 | Archive leaderboard | report |
| Image Generation | ImageNet 256x256 | StyleSAN-XL | FID | 2.14 | #52 of 94 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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