Diffusion-Guided Elite Path Inpainting for 3D Electromagnetic Coil Initialization

Electromagnetic coil design is a representative physical inverse-design problem: finding conductor geometries that achieve desired physical performance under geometric constraints. It underpins applications including power transfer, imaging, and induction heating. Although automatic synthesis is established for prescribed supports and parameterizations, many optimization workflows still require a manually supplied initial coil. We address this initialization gap by generating geometrically feasible candidate routes with high performance potential under a limited simulation budget. Our framework combines dual-view action diffusion with performance-preference-guided elite path reconstruction. Sequence and spatial views capture route order and three-dimensional occupancy, respectively. Quality-weighted residual learning from evaluated paths guides reconstruction while constraining deviations from a frozen geometry base. Hard depth-first search filters invalid actions and backtracks from dead ends; complete-path validation precedes evaluation and synchronous elite-archive updates. The archive maintains a pool of promising parents so that later rounds can build on evaluated candidates. We define a benchmark spanning symmetric enclosing, asymmetric enclosing, and non-enclosing scenes, three label budgets, and five repetitions. Averaged over five runs, our method leads the four learning baselines in Top-5@100 and Mean@100 across all nine settings, and in Best@100 in seven.