An Operator Analysis on Stochastic Differential Equation (SDE)-Based Diffusion Generative Models

Score-based generative models, grounded in stochastic differential equations (SDEs), excel in producing high-quality data but suffer from slow sampling due to the extensive nonlinear computations required for iterative score function evaluations. We propose an innovative approach that integrates score-based reverse SDEs with kernel methods, leveraging the derivative reproducing property of reproducing kernel Hilbert spaces (RKHSs) to efficiently approximate the eigenfunctions and eigenvalues of the Fokker–Planck operator. This enables data generation through linear combinations of eigenfunctions, transforming computationally intensive nonlinear operations into efficient linear ones, thereby significantly reducing computational overhead. Notably, our experimental results demonstrate remarkable progress: despite a slight reduction in sample diversity, the sampling time for a single image on the CIFAR-10 dataset is reduced to an impressive 0.29 s, marking a substantial advancement in efficiency. This work introduces novel theoretical and practical tools for generative modeling, establishing a robust foundation for real-time applications.