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.