# 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/fr/paper/2308.16534v1/

## Abstract

Score-based and diffusion models have emerged as effective approaches for both conditional and unconditional generation. Still conditional generation is based on either a specific training of a conditional model or classifier guidance, which requires training a noise-dependent classifier, even when the classifier for uncorrupted data is given. We propose an approach to sample from unconditional score-based generative models enforcing arbitrary logical constraints, without any additional training. Firstly, we show how to manipulate the learned score in order to sample from an un-normalized distribution conditional on a user-defined constraint. Then, we define a flexible and numerically stable neuro-symbolic framework for encoding soft logical constraints. Combining these two ingredients we obtain a general, but approximate, conditional sampling algorithm. We further developed effective heuristics aimed at improving the approximation. Finally, we show the effectiveness of our approach for various types of constraints and data: tabular data, images and time series.