Neural pruning, which involves identifying the optimal sparse subnetwork, is a key technique for reducing the complexity and improving the efficiency of deep neural networks. To address the challenge of solving neural pruning at a specific sparsity level directly, we investigate the evolution of optimal subnetworks with continuously increasing sparsity, which can provide insight into how to transform an unpruned dense model into an optimal subnetwork with any desired level of sparsity. In this paper, we proposed a novel pruning framework, coined Sparsity-indexed ODE (SpODE) that provides explicit guidance on how to best preserve model performance while ensuring an infinitesimal increase in model sparsity. On top of this, we develop a pruning algorithm, termed Pruning via Sparsity-indexed ODE (PSO), that enables effective pruning via traveling along the SpODE path. Empirical experiments show that PSO achieves either better or comparable performance compared to state-of-the-art baselines across various pruning settings.