Multi-arm motion planning is fundamental for enabling arms to complete complex long-horizon tasks in shared spaces efficiently but current methods struggle with scalability due to exponential state-space growth and reliance on large training datasets for learned models. Inspired by Multi-Agent Path Finding (MAPF), which decomposes planning into single-agent problems coupled with collision resolution, we propose a novel diffusion-guided multi-arm planner (DG-MAP) that enhances scalability of learning-based models while reducing their reliance on massive multi-arm datasets. Recognizing that collisions are primarily pairwise, we train two conditional diffusion models, one to generate feasible single-arm trajectories, and a second, to model the dual-arm dynamics required for effective pairwise collision resolution. By integrating these specialized generative models within a MAPF-inspired structured decomposition, our planner efficiently scales to larger number of arms. Evaluations against alternative learning-based methods across various team sizes demonstrate our method's effectiveness and practical applicability. Project website can be found at https://diff-mapf-mers.csail.mit.edu