Embodied agents operate in a structured world, often solving tasks with spatial, temporal, and permutation symmetries. Most algorithms for planning and model-based reinforcement learning (MBRL) do not take this rich geometric structure into account, leading to sample inefficiency and poor generalization. We introduce the Equivariant Diffuser for Generating Interactions (EDGI), an algorithm for MBRL and planning that is equivariant with respect to the product of the spatial symmetry group SE(3), the discrete-time translation group ℤ, and the object permutation group 𝕊ₙ. EDGI follows the Diffuser framework (Janner et. al 2022) in treating both learning a world model and planning in it as a conditional generative modeling problem, training a diffusion model on an offline trajectory dataset. We introduce a new SE(3) × ℤ × 𝕊ₙ-equivariant diffusion model that supports multiple representations. We integrate this model in a planning loop, where conditioning and classifier-based guidance allow us to softly break the symmetry for specific tasks as needed. On navigation and object manipulation tasks, \eqd improves sample efficiency and generalization.