Motion planning framed as optimisation in structured latent spaces has recently emerged as competitive with traditional methods in terms of planning success while significantly outperforming them in terms of computational speed. However, the real-world applicability of recent work in this domain remains limited by the need to express obstacle information directly in state-space, involving simple geometric primitives. In this work we address this challenge by leveraging learned scene embeddings together with a generative model of the robot manipulator to drive the optimisation process. In addition we introduce an approach for efficient collision checking which directly regularises the optimisation undertaken for planning. Using simulated as well as real-world experiments, we demonstrate that our approach, AMP-LS, is able to successfully plan in novel, complex scenes while outperforming competitive traditional baselines in terms of computation speed by an order of magnitude. We show that the resulting system is fast enough to enable closed-loop planning in real-world dynamic scenes.