Neurosymbolic Diffusion Models
Published in NeurIPS 2025
Authors: Emile van Krieken, Pasquale Minervini, Edoardo Ponti, Antonio Vergari
Project URL: https://openreview.net/forum?id=ifoKXDf1KS
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.
Bibtex:
@inproceedings{ krieken2025neurosymbolic, title={Neurosymbolic Diffusion Models}, author={Emile van Krieken and Pasquale Minervini and Edoardo Ponti and Antonio Vergari}, booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems}, year={2025}, url={https://openreview.net/forum?id=HfdzglsZQH} }