Neurosymbolic Diffusion Models

2025-05-19

AI Summary

Existing neural-symbolic (NeSy) predictors rely on the symbolic conditional independence assumption, leading to weak modeling of symbolic interactions, poor uncertainty quantification, and limited out-of-distribution (OOD) generalization. To address these limitations, we propose Neural-Symbolic Diffusion Models (NeSyDMs), the first NeSy framework incorporating discrete diffusion mechanisms. At each diffusion step, NeSyDMs reuse lightweight, independent modules to ensure scalability, while iterative denoising explicitly captures inter-symbol dependencies and propagates uncertainty. The model employs a dual-path inference architecture—visual and rule-based—to achieve symbol-level probabilistic calibration. Evaluated on visual path planning and rule-driven autonomous driving tasks, NeSyDMs achieve state-of-the-art accuracy among NeSy methods, with significant improvements in prediction calibration and OOD robustness.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Model symbol dependencies in neurosymbolic predictors
• Address overconfidence and poor out-of-distribution generalization
• Improve uncertainty quantification in symbolic reasoning tasks

Innovation

• NeSyDMs combine neural perception with symbolic reasoning
• Discrete diffusion models symbol dependencies and uncertainty
• Reuses independence assumption for scalable learning