Robots have been steadily increasing their presence in our daily lives, where they can work along with humans to provide assistance in various tasks on industry floors, in offices, and in homes. Automated assembly is one of the key applications of robots, and the next generation assembly systems could become much more efficient by creating collaborative human-robot systems. However, although collaborative robots have been around for decades, their application in truly collaborative systems has been limited. This is because a truly collaborative human-robot system needs to adjust its operation with respect to the uncertainty and imprecision in human actions, ensure safety during interaction, etc. In this paper, we present a system for human-robot collaborative assembly using learning from demonstration and pose estimation, so that the robot can adapt to the uncertainty caused by the operation of humans. Learning from demonstration is used to generate motion trajectories for the robot based on the pose estimate of different goal locations from a deep learning-based vision system. The proposed system is demonstrated using a physical 6 DoF manipulator in a collaborative human-robot assembly scenario. We show successful generalization of the system's operation to changes in the initial and final goal locations through various experiments.