Background and purpose: Although cone beam computed tomography (CBCT) enables online adaptive radiotherapy, its CT number accuracy may be insufficient for online adaptive proton therapy (OAPT). We compared proton dose distributions calculated directly on CBCT with calculations using additional CBCT image-processing methods in prostate cancer. Materials and methods: Retrospective proton plans were created for 10 prostate patients originally treated with 5-fraction online adaptive photon radiotherapy using CBCT. These plans were forward-calculated on each CBCT with four different approaches: (1) the clinical CBCT with a dedicated CT number calibration, (2) CBCT with histogram correction, (3) CT deformed to the CBCT, and (4) deformed CT with an air-cavity correction. Additionally, adaptive treatment using an OAPT workflow was simulated for each fraction and compared among the four CBCT-based methods. Dose-volume histograms (DVH) and related parameters were compared between the four methods for both non-adaptive and online adaptive treatment simulations. Results: Proton dose distributions were comparable across all CBCT-based strategies, with median differences of up to 1% for all DVH metrics compared to a reference method. Larger differences were observed for doses calculated directly on the CBCT for patient geometries deviating from the CBCT-specific calibration. Despite these differences, all four methods indicated the dosimetric benefits of OAPT over non-adaptive treatment. Conclusion: An advanced CBCT system enables proton dose calculations performed directly on the CBCT, demonstrating sufficient accuracy for integration into an OAPT workflow. Additional CBCT-based post-processing techniques are recommended to maximize the dosimetric benefit of plan adaptation in all patient populations.