Additive manufacturing (AM) provides a higher level of flexibility to build customized products with complex geometries, by selectively melting and solidifying metal powders. However, wide applications of AM beyond rapid prototyping are currently limited by its ability to perform quality assurance and control. Advanced melt-pool monitoring provides a unique opportunity to increase information visibility in the AM process. Stochastic melt-pool variations are closely pertinent to the quality of an AM build. There is a pressing need to investigate the variances of melt pools along the temporal scanning path, as well as within a 3D spatial neighborhood of the focal point by the laser beam. This paper presents a stochastic modeling framework to characterize and monitor spatiotemporal variations of melt-pool imaging data, including tensor decomposition of high-dimensional data, additive Gaussian process modeling of low-dimensional profiles as random variables, and hypothesis testing via the construction of confidence boundary for statistical process monitoring. Experimental results show the effectiveness of tensor decomposition for spatiotemporal monitoring of melt-pool variations in the metal-based AM process.