The Balmer-α line profile observed from high-temperature magnetized plasmas can be interpreted as the sum of narrow and broad components corresponding to the emission from atoms generated in edge and core regions, respectively. The inversion of this line profile reveals the atom density distribution in the plasma. The inversion method we reported in previous studies [Nucl. Fusion, 55, 063029 (2015) and Rev. Sci. Instrum., 85, 023502 (2014)] requires a regularization parameter that must be manually tuned to avoid overfitting. Therefore, it has been difficult to evaluate the uncertainty of the results. Here, we report an improved method based on Bayesian statistics in which the regularization parameter is interpreted as an adjustable parameter, which is then marginalized for the uncertainty evaluation. Two types of prior distributions were examined. The first is an empirical prior that assumes the smoothness of a solution, and the second is based on a diffusion model of hydrogen atoms. We found the use of the diffusion model as prior information to have an advantage with respect to the accuracy of the core region atom density.