Abstract: Accurately predicting the remaining useful life (RUL) of lithium-ion batteries is crucial for safe operation. Grey prediction models, with advantages in handling small samples and uncertain information, offer a promising approach for RUL prediction. However, most of the existing grey prediction models focus on the degradation trend while neglecting the capacity regeneration phenomenon. To address this limitation, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is first applied to separate the capacity degradation trend from local regeneration trends, addressing their differences in magnitude and characteristics. A hybrid prediction method, which combines an improved grey multivariate model and Bayesian-optimized Gaussian process regression, is then proposed. For the capacity degradation trend, which exhibits information heterogeneity and an exponential nonlinear trend, a variable new information priority fractional discrete grey multivariate model is proposed for prediction. The model is not only based on the ideas of variable-order accumulation and discrete grey models, but also introduces an additional nonlinear correction term. For the local regeneration trend, which is nonstationary, nonlinear, and noisy, a denoising autoencoder is employed for noise reduction and feature enrichment, followed by the Bayesian-optimized Gaussian process regression model for prediction. Finally, the predictions of each component are reconstructed to obtain the complete capacity sequence. Multidimensional evaluations on multiple NASA battery datasets, including comparisons with common baseline models and ablation studies to verify the effectiveness of each module, demonstrate that the proposed method achieves superior accuracy, stability, and generalization in capacity degradation prediction.