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

TL;DR

This paper presents Neuro-Symbolic Diffusion (NSD), a framework that combines diffusion models with symbolic optimization to generate physically grounded, safe, and constraint-compliant samples across various domains.

Contribution

The introduction of NSD, enabling the first integration of symbolic constraints with diffusion models for both continuous and discrete data generation.

Findings

Successfully generates non-toxic molecules and collision-free trajectories.

Improves data efficiency in drug discovery and materials engineering.

Enables out-of-domain generalization through symbolic constraint enforcement.

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.