This paper presents a domain-adaptive self-rewarded generative adversarial network (SRWGAN) for multi-pair bidirectional cross-modality image translation. Cross-modality bidirectional translation remains a challenging problem in AI because it requires learning consistent mappings and maintaining feature and cross-domain consistency across multiple imaging domains. While GAN-based methods are popular for cross-modality translation, employing separate generators ( \(G\) ) for each direction increases complexity and limits scalability. Moreover, they struggle to adapt to different domains and to generalize across diverse datasets. In addition, traditional \(\:G\) have limited flexibility and depend heavily on discriminator ( \(D\) ) feedback, which often leads to superficial imitation instead of learning accurate modality-specific representations. This work introduces a domain-adaptive SRWGAN with a single generator that leverages a RewardNet to create its own feedback, guiding and improving the translation process. This self-rewarding system gives the \(G\) more autonomy, enabling it to improve performance without depending entirely on the \(D\) . The model also incorporates a dual extremum activation function (DEAF), helping the \(\:D\) better distinguishes between differences. The model can handle bidirectional translation across a variety of medical imaging types, such as MRI ↔ PET, SRS ↔ H&E, CT ↔ MRI, and SPECT ↔ MRI. The model is evaluated on ten metrics, including SSIM and DSSIM, and its self-rewarding mechanism helps better align features across modalities, improving overall translation quality. Additionally, Grad-CAM analysis visualized the key regions of emphasis during translation. This bidirectional cross-modality translation SRWGAN uses a self-rewarding mechanism to boost performance, flexibility, and scalability across diverse imaging datasets.