Contrastive Sampling Chains in Diffusion Models

The past few years have witnessed great success in the use of diffusion models (DMs) to generate high-fidelity images with the help of stochastic differential equations (SDEs). However, discretization error is an inevitable limitation when utilizing numerical solvers to solve SDEs. To address this limitation, we provide a theoretical analysis demonstrating that an appropriate combination of the contrastive loss and score matching serves as an upper bound of the KL divergence between the true data distribution and the model distribution. To obtain this bound, we utilize a contrastive loss to construct a contrastive sampling chain to fine-tuning the pre-trained DM. In this manner, our method reduces the discretization error and thus yields a smaller gap between the true data distribution and our model distribution. Moreover, the presented method can be applied to fine-tuning various pre-trained DMs, both with or without fast sampling algorithms, contributing to better sample quality or slightly faster sampling speeds. To validate the efficacy of our method, we conduct comprehensive experiments. For example, on CIFAR10, when applied to a pre-trained EDM, our method improves the FID from 2.04 to 1.88 with 35 neural function evaluations (NFEs), and reduces NFEs from 35 to 25 to achieve the same 2.04 FID.