Neurosymbolic Diffusion Models

TL;DR

Neurosymbolic diffusion models (NeSyDMs) enhance traditional neural-symbolic predictors by modeling symbol dependencies with diffusion processes, leading to improved accuracy and uncertainty estimation in visual reasoning tasks.

Contribution

Introduction of NeSyDMs that incorporate discrete diffusion to model dependencies between symbols, overcoming independence limitations of prior NeSy predictors.

Findings

Achieve state-of-the-art accuracy on benchmarks

Demonstrate strong calibration and uncertainty quantification

Effective in high-dimensional visual tasks

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.