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

Jacob K. Christopher, Michael Cardei, Jinhao Liang, Ferdinando Fioretto
Proceedings of the International Conference on Neuro-symbolic Systems, PMLR 288:188-213, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v288-christopher25a, title = {Neuro-Symbolic Generative Diffusion Models for Physically Grounded, Robust, and Safe Generation}, author = {Christopher, Jacob K. and Cardei, Michael and Liang, Jinhao and Fioretto, Ferdinando}, booktitle = {Proceedings of the International Conference on Neuro-symbolic Systems}, pages = {188--213}, year = {2025}, editor = {Pappas, George and Ravikumar, Pradeep and Seshia, Sanjit A.}, volume = {288}, series = {Proceedings of Machine Learning Research}, month = {28--30 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v288/main/assets/christopher25a/christopher25a.pdf}, url = {https://proceedings.mlr.press/v288/christopher25a.html}, 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.} }
Endnote
%0 Conference Paper %T Neuro-Symbolic Generative Diffusion Models for Physically Grounded, Robust, and Safe Generation %A Jacob K. Christopher %A Michael Cardei %A Jinhao Liang %A Ferdinando Fioretto %B Proceedings of the International Conference on Neuro-symbolic Systems %C Proceedings of Machine Learning Research %D 2025 %E George Pappas %E Pradeep Ravikumar %E Sanjit A. Seshia %F pmlr-v288-christopher25a %I PMLR %P 188--213 %U https://proceedings.mlr.press/v288/christopher25a.html %V 288 %X 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.
APA
Christopher, J.K., Cardei, M., Liang, J. & Fioretto, F.. (2025). Neuro-Symbolic Generative Diffusion Models for Physically Grounded, Robust, and Safe Generation. Proceedings of the International Conference on Neuro-symbolic Systems, in Proceedings of Machine Learning Research 288:188-213 Available from https://proceedings.mlr.press/v288/christopher25a.html.

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