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.

我们提出了一种梯度流程用于生成建模，通过将粒子从初始源分布传输到目标分布，其中粒子上的梯度场由噪声自适应最大均值差异 (MMD) 的梯度给出。我们称该方法为扩散 - MMD - 梯度流或 DMMD。该方法不需要对抗性训练，而与生成对抗网络 (GAN) 中的判别器训练相关。我们在 CIFAR10、MNIST、CELEB-A (64 x64) 和 LSUN Church (64 x 64) 的无条件图像生成中获得了具有竞争力的实证性能，并在 MMD 被 KL 散度的下界替代时证明了该方法的有效性。