Abstract: In photon-counting computerized tomography (PCCT), the detector can only receive partial photon energy within a single energy channel, resulting in limited photon counting rates and a significantly reduced signal-to-noise ratio of the projection data. Aiming at the limitation that strongly supervised denoising methods rely on large-scale paired datasets and to address the issue that weakly supervised methods using unpaired data have insufficient denoising performance, this study proposes a weakly supervised projection denoising method based on an optimal transport network. The method first adaptively matches the noise and reference distributions by constructing an optimal transport constraint term for projection data consistency. Second, an optimal transport generative adversarial network framework integrated with attention mechanisms was designed to synchronously optimize noise suppression and detail recovery capabilities under unpaired training conditions. Finally, the framework was used to process noisy projections and perform image reconstruction, verifying the feature consistency transfer from the projection to the image domain. In experiments, compared with mainstream denoising methods, the proposed method achieved a peak signal-to-noise ratio improvement of 0.47 dB and increased the structural similarity from 0.75 to 0.81 on the PCCT projection dataset. This study provides a robust denoising solution for PCCT imaging that does not require precisely paired datasets.