Neurosymbolic Diffusion Models

Neurosymbolic (NeSy) predictors combine neural perception with symbolicreasoning to solve tasks like visual reasoning. However, standard NeSypredictors assume conditional independence between the symbols they extract,thus limiting their ability to model interactions and uncertainty - oftenleading to overconfident predictions and poor out-of-distributiongeneralisation. To overcome the limitations of the independence assumption, weintroduce neurosymbolic diffusion models (NeSyDMs), a new class of NeSypredictors that use discrete diffusion to model dependencies between symbols.Our approach reuses the independence assumption from NeSy predictors at eachstep of the diffusion process, enabling scalable learning while capturingsymbol dependencies and uncertainty quantification. Across both synthetic andreal-world benchmarks - including high-dimensional visual path planning andrule-based autonomous driving - NeSyDMs achieve state-of-the-art accuracy amongNeSy predictors and demonstrate strong calibration.