Aadithya Srikanth

Aadithya Srikanth, Siddarth Asokan, Nishanth Shetty et al.

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.

Aadithya Srikanth, Mudit Gaur, Vaneet Aggarwal

Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(ε^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.