2024/05/10 by Alexandre Galashov, Valentin De Bortoli, Galashov, Alexandre +3 · 2 citations
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Fluid Dynamics and Turbulent Flows #Machine Learning (cs.LG) #Plasma and Flow Control in Aerodynamics
paper · pdf · doi:10.48550/arxiv.2405.06780
openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.