We develop a technique for generating smooth and accurate 3D human pose and motion estimates from RGB video sequences. Our technique, which we call Motion Estimation via Variational Autoencoder (MEVA), decomposes a temporal sequence of human motion into a smooth motion representation using auto-encoder-based motion compression and a residual representation learned through motion refinement. This two-step encoding of human motion captures human motion in two stages: a general human motions estimation step that captures the coarse overall motion, and a residual estimation that adds back person-specific motion details. Experiments show that our method produces both smooth and accurate 3D human pose and motion estimates.