Score-based Generative Models (SGMs) have achieved remarkable success in generation tasks by establishing a diffusion process that gradually perturbs real data into Gaussian noise and then learning a reverse process to reconstruct the data from noise. However, conventional denoising methods, such as Langevin dynamics and numerical stochastic differential equation solvers, rely on randomness but suffer from slow generation speeds due to the high number of score function evaluations. To address this, we propose a plug-and-play Markov adaptive momentum sampling method, inspired by the strong connection between the SGMs' sampling process and stochastic gradient descent optimization. Our approach accelerates the transformation process without introducing additional hyperparameters. Theoretically, we establish a rigorous foundation by analyzing the relationship between the distribution of samples generated by our method and the original data distribution. This provides a novel perspective on the analysis of sampling distributions. Empirically, our method demonstrates superior efficiency, generating high-quality images/graphs in significantly fewer sampling steps, achieving a speedup of 2x to 5x while maintaining or surpassing baseline performance on various image and graph generation benchmarks. These results underscore the effectiveness of adaptive momentum in enhancing the efficiency of SGMs.

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