This paper explores the challenge of accelerating the sequential inference process of Diffusion Probabilistic Models (DPMs). We tackle this critical issue from a dynamic systems perspective, in which the inherent sequential nature is transformed into a parallel sampling process. Specifically, we propose a unified framework that generalizes the sequential sampling process of DPMs as solving a system of banded nonlinear equations. Under this generic framework, we reveal that the Jacobian of the banded nonlinear equations system possesses a unit-diagonal structure, enabling further approximation for acceleration. Moreover, we theoretically propose an effective initialization approach for parallel sampling methods. Finally, we construct \textit{ParaSolver}, a hierarchical parallel sampling technique that enhances sampling speed without compromising quality. Extensive experiments show that ParaSolver achieves up to \textbf{12.1× speedup} in terms of wall-clock time. The source code is publicly available at https://github.com/Jianrong-Lu/ParaSolver.git.