The wireless channel response contains rich multipath information, but accurately extracting this information remains challenging in complex indoor environments. In this paper, we propose a deep learning-based sparse recovery method for super-resolution multipath time delay estimation (TDE) and dictionary mismatch mitigation in sparse modeling. The proposed DenoisingCNN framework recovers the sparse delay spectrum from the channel response with highly overlapping multipath components (MPCs) with three specialized modules to addressing dictionary mismatch. Numerical experiments demonstrate that the proposed method outperforms current state-of-the-art approaches in the estimation of both the number of paths and the multipath time delays, offering robustness and strong generalization capabilities.