Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data.

We integrate this model in a planning loop, where conditioning and classifier guidance let us softly break the symmetry for specific tasks as needed.

These papers focus on building the symmetries into the models by modifying the architecture.

In the natural sciences, physics has found great success by describing the universe in terms of symmetry preserving transformations. Inspired by this formalism, we propose a framework, built upon the theory of group representation, for learning representations of a dynamical environment structured around the transformations that generate its evolution. Experimentally, we learn the structure of explicitly symmetric environments without supervision from observational data generated by sequential interactions.

Symmetry has been a fundamental tool in the exploration of a broad range of complexsystems.