# Conditioning Score-Based Generative Models by Neuro-Symbolic Constraints

**Authors:** Davide Scassola, Sebastiano Saccani, Ginevra Carbone, Luca Bortolussi  
**arXiv:** [2308.16534](https://arxiv.org/abs/2308.16534)  
**Date:** 2023-08-31  
**Summary page:** https://www.summarizepaper.com/en/paper/2308.16534v1/

## Key points

- The paper discusses the use of score-based and diffusion models for conditional and unconditional generation
- Proposes a novel approach to sample from unconditional score-based generative models with logical constraints without additional training
- Introduces a flexible and numerically stable neuro-symbolic framework for encoding soft logical constraints
- Develops a general but approximate conditional sampling algorithm by combining the learned score manipulation and neuro-symbolic framework
- Effective heuristics are developed to improve the approximation
- Demonstrates effectiveness through experiments on tabular data, images, and time series
- Successfully enforces logical constraints in generated samples
- Eliminates the need for additional training or classifier guidance
- Provides flexibility in enforcing arbitrary logical constraints
- Experimental results validate effectiveness across different types of data

## Summary

The paper titled "Conditioning Score-Based Generative Models by Neuro-Symbolic Constraints" discusses the use of score-based and diffusion models for conditional and unconditional generation. This paper proposes a novel approach to sample from unconditional score-based generative models with arbitrary logical constraints without any additional training. The authors demonstrate how to manipulate the learned score to sample from an un-normalized distribution based on a user-defined constraint and introduce a flexible and numerically stable neuro-symbolic framework for encoding soft logical constraints. By combining these two components, they develop a general but approximate conditional sampling algorithm. Effective heuristics are also developed to improve the approximation. The effectiveness of the proposed approach is demonstrated through experiments on various types of data, including tabular data, images, and time series. The results show that the method successfully enforces logical constraints in the generated samples. Overall, this paper presents a novel method for conditioning score-based generative models using neuro-symbolic constraints which eliminates the need for additional training or classifier guidance and provides flexibility in enforcing arbitrary logical constraints. The experimental results validate the effectiveness of the proposed method across different types of data.