We present a lightweight solution to recover 3D pose from multi-view images captured with spatially calibrated cameras. Building upon recent advances in interpretable representation learning, we exploit 3D geometry to fuse input images into a unified latent representation of pose, which is disentangled from camera view-points. This allows us to reason effectively about 3D pose across different views without using compute-intensive volumetric grids. Our architecture then conditions the learned representation on camera projection operators to produce accurate per-view 2d detections, that can be simply lifted to 3D via a differentiable Direct Linear Transform (DLT) layer. In order to do it efficiently, we propose a novel implementation of DLT that is orders of magnitude faster on GPU architectures than standard SVD-based triangulation methods. We evaluate our approach on two large-scale human pose datasets (H36M and Total Capture): our method outperforms or performs comparably to the state-of-the-art volumetric methods, while, unlike them, yielding real-time performance.