Neurosymbolic Diffusion Models

Emile van Krieken, Pasquale Minervini, Edoardo Ponti, Antonio Vergari

Keywords: neurosymbolic AI, discrete diffusion models, probabilistic reasoning, uncertainty, reasoning shortcuts

TL;DR: We integrate discrete diffusion models with neurosymbolic predictors for scalable and calibrated learning and reasoning

Abstract: 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.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 12204