Manual uncertainty propagation from possible noise sources has often been adopted for data analysis in many fields of science, including the analysis of Thomson scattering measurement data in fusion plasma science. However, it is not possible to perfectly model all the noise sources and their distributions. In this work, we propose a more data-driven approach for the noise modeling of multichannel measurement systems. We directly modeled the noise distribution by tractable density distributions parameterized with neural networks and trained their weights from a vast amount of measurement data. We demonstrated an application of this method in Thomson scattering measurement data for the Large Helical Device project. This method enabled us to make a realistic inference even without sufficient prior knowledge about the noise.