  Non-Abelian braiding has attracted substantial attention because of its
pivotal role in describing the exchange behaviour of anyons, in which the input
and outcome of non-Abelian braiding are connected by a unitary matrix.
Implementing braiding in a classical system can assist the experimental
investigation of non-Abelian physics. However, the design of non-Abelian gauge
fields faces numerous challenges stemmed from the intricate interplay of group
structures, Lie algebra properties, representation theory, topology, and
symmetry breaking. The extreme diversity makes it a powerful tool for the study
of condensed matter physics. Whereas the widely used artificial intelligence
with data-driven approaches has greatly promoted the development of physics,
most works are limited on the data-to-data design. Here we propose a
self-reasoning assistant learning framework capable of directly generating
non-Abelian gauge fields. This framework utilizes the forward diffusion process
to capture and reproduce the complex patterns and details inherent in the
target distribution through continuous transformation. Then the reverse
diffusion process is used to make the generated data closer to the distribution
of the original situation. Thus, it owns strong self-reasoning capabilities,
allowing to automatically discover the feature representation and capture more
subtle relationships from the dataset. Moreover, the self-reasoning eliminates
the need for manual feature engineering and simplifies the process of model
building. Our framework offers a disruptive paradigm shift to parse complex
physical processes, automatically uncovering patterns from massive datasets.
