Deep MMD Gradient Flow without adversarial training

One challenge that arises when applying these models in practice is that the Stein score (that is, the gradient log We propose a gradient flow procedure for generative of the current noisy density) becomes ill-behaved near the modeling by transporting particles from an data distribution (Yang et al., 2023): the diffusion process initial source distribution to a target distribution, needs to be slowed down at this point, which incurs a large where the gradient field on the particles is given number of sampling steps near the data distribution. Indeed, by a noise-adaptive Wasserstein Gradient of the if the manifold hypothesis holds (Tenenbaum et al., 2000; Maximum Mean Discrepancy (MMD). The noiseadaptive Fefferman et al., 2016; Brown et al., 2022) and the data MMD is trained on data distributions corrupted is supported on a lower dimensional space, it is expected by increasing levels of noise, obtained via that the score will explode for noise levels close to zero, a forward diffusion process, as commonly used to ensure that the backward process concentrates on this in denoising diffusion probabilistic models. The lower dimensional manifold (Bortoli, 2023; Pidstrigach, result is a generalization of MMD Gradient Flow, 2022; Chen et al., 2022). While strategies exist to mitigate which we call Diffusion-MMD-Gradient Flow or these issues, they trade-off the quality of the output against DMMD. The divergence training procedure is inference speed, see for instance (Song et al., 2023; Xu et al., related to discriminator training in Generative Adversarial 2023; Sauer et al., 2023). Networks (GAN), but does not require adversarial training. We obtain competitive empirical Generative Adversarial Networks (GANs) (Goodfellow performance in unconditional image generation et al., 2014) represent an alternative popular generative modelling on CIFAR10, MNIST, CELEB-A (64 x64) framework (Brock et al., 2019; Karras et al., 2020a).