Coherent Anti-Stokes Raman Spectroscopy (CARS) provides non-invasive, label-free chemical analysis at high spatial resolution, making it a powerful tool for biomedical and material imaging. However, their effectiveness is hindered by a dominant and unpredictable non-resonant background (NRB) that distorts meaningful spectral features. Existing NRB removal methods often require additional measurements or computationally intensive post-processing. In this work, we present a physics-informed framework that leverages the broadband, low-rank structure of the NRB using Dynamic Mode Decomposition (DMD) for unsupervised separation of resonant Raman modes from non-resonant contributions in the spectral domain. We further introduce DA-DMD - a Deep Learning-Assisted DMD approach, that uses an attention mechanism to adaptively weight DMD modes and a CNN with skip connection to enhance Raman signal reconstruction. Trained entirely on synthetic data, DA-DMD eliminates the need for experimental labels or calibration. We validate our methods on synthetic and real CARS measurements, demonstrating superior background suppression, fidelity preservation, and generalization compared to existing approaches. DA-DMD offers fast inference and improves robustness, positioning it as a practical tool for scalable chemical imaging in complex environments.