Neuro-Symbolic Generative Diffusion Models for Physically Grounded, Robust, and Safe Generation

2025-06-01

AI Summary

Diffusion models struggle to strictly satisfy physical, logical, and functional constraints in safety-critical and scientific applications. To address this, we propose the Neural-Symbolic Generative Diffusion Model—the first framework enabling certified co-execution of diffusion sampling and symbolic reasoning. Our approach integrates constraint-driven latent-space optimization, a differentiable symbolic solver, and a dual discrete/continuous path architecture to dynamically embed symbolic optimization into the diffusion process, ensuring verifiably consistent generation. It unifies constrained generation across both continuous modalities (e.g., robot trajectories) and discrete ones (e.g., molecules, text). Experiments demonstrate substantial improvements in safety, robustness, and physical consistency across diverse tasks: non-toxic molecular design, collision-free trajectory planning, few-shot materials discovery, and cross-domain generalization.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Diffusion Models for Vision
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Agentic search

Abstract

Despite the remarkable generative capabilities of diffusion models, their integration into safety-critical or scientifically rigorous applications remains hindered by the need to ensure compliance with stringent physical, structural, and operational constraints. To address this challenge, this paper introduces Neuro-Symbolic Diffusion (NSD), a novel framework that interleaves diffusion steps with symbolic optimization, enabling the generation of certifiably consistent samples under user-defined functional and logic constraints. This key feature is provided for both standard and discrete diffusion models, enabling, for the first time, the generation of both continuous (e.g., images and trajectories) and discrete (e.g., molecular structures and natural language) outputs that comply with constraints. This ability is demonstrated on tasks spanning three key challenges: (1) Safety, in the context of non-toxic molecular generation and collision-free trajectory optimization; (2) Data scarcity, in domains such as drug discovery and materials engineering; and (3) Out-of-domain generalization, where enforcing symbolic constraints allows adaptation beyond the training distribution.

Problem

• Ensures generative models comply with physical and safety constraints
• Integrates symbolic optimization with diffusion for consistent outputs
• Addresses safety, data scarcity, and out-of-domain generalization challenges

Innovation

• Neuro-Symbolic Diffusion interleaves diffusion with symbolic optimization
• Generates continuous and discrete outputs with constraints
• Ensures safety, data scarcity handling, and generalization