Galashov, alexandre; De Bortoli, Valentin; Gretton, Arthur; (2025) Deep MMD Gradient Flow without adversarial training. In: Proceedings 13th International Conference on Learning Representations ICLR 2025. ICLR: Singapore, Singapore. (In press).

Text 5199_Deep_MMD_Gradient_Flow_wi.pdf - Published Version Access restricted to UCL open access staff until 25 October 2025. Download (23MB)

Abstract

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.

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