Deep MMD Gradient Flow without adversarial training
This provides a non-adversarial alternative to GANs for generative modeling, though it appears incremental as it builds on existing diffusion and MMD techniques.
The authors tackled generative modeling by proposing Diffusion-MMD-Gradient Flow (DMMD), a gradient flow method that transports particles using a noise-adaptive Wasserstein gradient of MMD without adversarial training, achieving competitive image generation results on datasets like CIFAR10 and MNIST.
We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise-adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.