Insights into Closed-form IPM-GAN Discriminator Guidance for Diffusion Modeling

Diffusion models are a state-of-the-art generative modeling framework that transform noise to images via Langevin sampling, guided by the score, which is the gradient of the logarithm of the data distribution. Recent works have shown empirically that the generation quality can be improved when guided by classifier network, which is typically the discriminator trained in a generative adversarial network (GAN) setting. In this paper, we propose a theoretical framework to analyze the effect of the GAN discriminator on Langevin-based sampling, and show that the IPM-GAN optimization can be seen as one of smoothed score-matching, wherein the scores of the data and the generator distributions are convolved with the kernel function associated with the IPM. The proposed approach serves to unify score-based training and optimization of IPM-GANs. Based on these insights, we demonstrate that closed-form kernel-based discriminator guidance, results in improvements (in terms of CLIP-FID and KID metrics) when applied atop baseline diffusion models. We demonstrate these results on the denoising diffusion implicit model (DDIM) and latent diffusion model (LDM) settings on various standard datasets. We also show that the proposed approach can be combined with existing accelerated-diffusion techniques to improve latent-space image generation.