Diffusion models have demonstrated remarkable success in generative tasks, yet their iterative denoising process results in slow inference, limiting their practicality. While existing acceleration methods exploit the well-known U-shaped similarity pattern between adjacent steps through caching mechanisms, they lack theoretical foundation and rely on simplistic computation reuse, often leading to performance degradation. In this work, we provide a theoretical understanding by analyzing the denoising process through the second-order Adams-Bashforth method, revealing a linear relationship between the outputs of consecutive steps. This analysis explains why the outputs of adjacent steps exhibit a U-shaped pattern. Furthermore, extending Adams-Bashforth method to higher order, we propose a novel caching-based acceleration approach for diffusion models, instead of directly reusing cached results, with a truncation error bound of only (O(hk) where h is the step size. Extensive validation across diverse image and video diffusion models (including HunyuanVideo and FLUX.1-dev) with various schedulers demonstrates our method's effectiveness in achieving nearly 3× speedup while maintaining original performance levels, offering a practical real-time solution without compromising generation quality.