This paper proposes an unsupervised DNN-based speech enhancement approach founded on deep priors (DPs). Here, DP signifies that DNNs are more inclined to produce clean speech signals than noises. Conventional methods based on DP typically involve training on a noisy speech signal using a random noise feature as input, stopping training only a clean speech signal is generated. However, such conventional approaches encounter challenges in determining the optimal stop timing, experience performance degradation due to environmental background noise, and suffer a trade-off between distortion of the clean speech signal and noise reduction performance. To address these challenges, we utilize two DNNs: one to generate a clean speech signal and the other to generate noise. The combined output of these networks closely approximates the noisy speech signal, with a loss term based on spectral kurtosis utilized to separate the noisy speech signal into a clean speech signal and noise. The key advantage of this method lies in its ability to circumvent trade-offs and early stopping problems, as the signal is decomposed by enough steps. Through evaluation experiments, we demonstrate that the proposed method outperforms conventional methods in the case of white Gaussian and environmental noise while effectively mitigating early stopping problems.