  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)xZxSn-equivariant diffusion
model that supports multiple representations. We integrate this model in a
planning loop, where conditioning and classifier guidance let us softly break
the symmetry for specific tasks as needed. On object manipulation and
navigation tasks, EDGI is substantially more sample efficient and generalizes
better across the symmetry group than non-equivariant models.
