让扩散模型生成符合物理规则的可靠结果，突破安全与数据稀缺瓶颈
Neuro-Symbolic Generative Diffusion Models for Physically Grounded, Robust, and Safe Generation
- 扩散过程穿插符号优化，确保生成内容满足用户定义的约束
- 首次实现连续与离散输出在约束下的可验证一致性，如分子结构和轨迹
- 适合安全敏感场景，如药物设计、机器人路径规划等
尽管扩散模型具备强大的生成能力，但在安全关键或科学严谨的应用中仍受限于难以保证物理、结构及操作约束的合规性。本文提出神经符号扩散（NSD）框架，将扩散步骤与符号优化交替进行，实现用户自定义功能与逻辑约束下可验证一致的样本生成。该方法适用于标准与离散扩散模型，首次支持连续（如图像、轨迹）与离散（如分子结构、自然语言）输出在约束下的生成。在三大挑战中验证：(1) 安全性，如生成无毒分子与无碰撞轨迹；(2) 数据稀缺，如药物发现与材料工程；(3) 非域泛化，通过符号约束实现对训练分布外数据的适应。
原文摘要 · Abstract (English)
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.
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