Volumetric phenomena, such as clouds and fog, present a significant challenge for 3D reconstruction systems due to their translucent nature and their complex interactions with light. Conventional techniques for reconstructing scattering volumes rely on controlled setups, limiting practical applications. This paper introduces an approach to reconstructing volumes from a few input stereo pairs. We propose a novel deep learning framework that integrates a deep stereo model with a 3D Convolutional Neural Network (3D CNN) and an advection module, capable of capturing the shape and dynamics of volumes. The stereo depths are used to carve empty space around volumes, providing the 3D CNN with a prior for coping with the lack of input views. Refining our output, the advection module leverages the temporal evolution of the medium, providing a mechanism to infer motion and improve temporal consistency. The efficacy of our system is demonstrated through its ability to estimate density and velocity fields of large-scale volumes, in this case, clouds, from a sparse set of stereo image pairs.