In this paper, we transfer machine learning techniques previously applied to denoising surface-only Monte Carlo renderings to path-traced visualizations of medical volumetric data. In the domain of medical imaging, path-traced videos turned out to be an efficient means to visualize and understand internal structures, in particular for less experienced viewers such as students or patients. However, the computational demands for the rendering of high-quality path-traced videos are very high due to the large number of samples necessary for each pixel. To accelerate the process, we present a learning-based technique for denoising path-traced videos of volumetric data by increasing the sample count per pixel; both through spatial (integrating neighboring samples) and temporal filtering (reusing samples over time). Our approach uses a set of additional features and a loss function both specifically designed for the volumetric case. Furthermore, we present a novel network architecture tailored for our purpose, and introduce reprojection of samples to improve temporal stability and reuse samples over frames. As a result, we achieve good image quality even from severely undersampled input images, as visible in the teaser image.