Neurosymbolic Diffusion Models
Authors: name: Emile van Krieken, name: Pasquale Minervini, name: Edoardo Ponti, name: Antonio Vergari

Neurosymbolic (NeSy) predictors combine neural perception with symbolic
reasoning to solve tasks like visual reasoning. However, standard NeSy
predictors assume conditional independence between the symbols they extract,
thus limiting their ability to model interactions and uncertainty - often
leading to overconfident predictions and poor out-of-distribution
generalisation. To overcome the limitations of the independence assumption, we
introduce neurosymbolic diffusion models (NeSyDMs), a new class of NeSy
predictors that use discrete diffusion to model dependencies between symbols.
Our approach reuses the independence assumption from NeSy predictors at each
step of the diffusion process, enabling scalable learning while capturing
symbol dependencies and uncertainty quantification. Across both synthetic and
real-world benchmarks - including high-dimensional visual path planning and
rule-based autonomous driving - NeSyDMs achieve state-of-the-art accuracy among
NeSy predictors and demonstrate strong calibration.