Energy-based Compositional Diffusion Planning

Compositional diffusion planners enable robotic decision-making beyond the horizon of training trajectories. Yet, current approaches often rely on the heuristic stitching of local predictions. We demonstrate that this induces a non-conservative vector field that does not mathematically correspond to any valid global trajectory log-density function. We propose Energy-based Compositional Diffuser (ECD), a framework that formulates the global trajectory as the minimizer of the sum of local bridge potentials. This energy-based perspective guarantees a conservative update field by construction and reveals a critical endpoint reaction term that is missing in heuristic stitching methods. To enable efficient inference, we further introduce a Markov-based score approximation that computes the reaction term though a single block-tridiagonal solve, maintaining time complexity linear in the planning horizon. Empirically, ECD achieves state-of-the-art success rates on a range of OGBench stitching tasks, while nearly matching the inference speed of heuristic stitching methods.