Low-light image enhancement poses a significant challenge due to the limited information captured by image sensors in low-light environments. Despite recent improvements in deep learning models, the lack of paired training datasets remains a significant obstacle. Therefore, unsupervised methods have emerged as a promising solution. In this work, we focus on the strength of curve-adjustment-based approaches to tackle unsupervised methods. The majority of existing unsupervised curve-adjustment approaches iteratively estimate higher order curve parameters to enhance the exposure of images while efficiently preserving the details of the images. However, the convergence of the enhancement procedure cannot be guaranteed, leading to sensitivity to the number of iterations and limited performance. To address this problem, we consider the iterative curve-adjustment update process as a dynamic system and formulate it as a Neural Ordinary Differential Equations (NODE) for the first time, and this allows us to learn a continuous dynamics of the latent image. The strategy of utilizing NODE to leverage continuous dynamics in iterative methods enhances unsupervised learning and aids in achieving better convergence compared to discrete-space approaches. Consequently, we achieve state-of-the-art performance in unsupervised low-light image enhancement across various benchmark datasets.