Traditional calibration transfer (CT) methods usually fail to adapt the source domain model to the target domain because of changes associated with the instrument, detection environment, sample composition, or sample type. Most deep transfer learning (DTL) methods have shown reliable capability in extracting domain-invariant representations. However, factors unique to the spectral domain limit their development and application, including difficulty in obtaining labeled samples, numerous spectral perturbation factors, and the scarcity of spectral databases. To address these challenges, we here introduce the Bidirectional Domain-Separating Adversarial Network (BiDSAN), based on a deep adversarial network transfer architecture, for learning and adapting to distribution/domain differences between sample spectra. BiDSAN incorporates Wasserstein divergence (w-div) and dynamic adversarial factor into the domain critic (discriminator) to accelerate the extraction of spectral shared components. Additionally, the use of the spectral signal distortion ratio as a loss function and the introduction of a bidirectional mechanism further enhanced the training accuracy and speed of spectral models. Calibration analyses were tested on pharmaceutical and two sets of wood datasets, corresponding to three common domain/distribution difference scenarios discussed in the study. Compared to existing CT and DTL methods, the proposed BiDSAN method demonstrated superior spectral signal calibration capability and stability, achieving unsupervised domain adaptation for similar samples and, for the first time, obtaining ideal prediction results in cross-species spectral domain adaptation. Our method represents significant potential for using DTL approaches in spectral domain adaptation.