# Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraints

arXiv: https://arxiv.org/abs/2308.16534 · HTML: https://mlsanity.com/paper/2308.16534/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Latent Constraints: Learning to Generate Conditionally from Unconditional Generative Models](https://mlsanity.com/paper/1711.05772/) (2017)
- [logLTN: Differentiable Fuzzy Logic in the Logarithm Space](https://mlsanity.com/paper/2306.14546/) (2023)

## Built on by (most cited first, 7 of 7)

- [A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyond](https://mlsanity.com/paper/2503.05954/) (2025)
- [Incantation: Natural Language as the Action Interface for Multi-Entity Video World Models](https://mlsanity.com/paper/2605.18601/) (2026)
- [Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI](https://mlsanity.com/paper/2510.25497/) (2025)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)
- [Harpoon: Generalised Manifold Guidance for Conditional Tabular Diffusion](https://mlsanity.com/paper/2602.07875/) (2026)
- [Guiding Neuro-Symbolic Scenario Generation with Spatio-Temporal Logic](https://mlsanity.com/paper/2605.19038/) (2026)
- [Parallel Noising in Neural Markov Logic Networks](https://mlsanity.com/paper/2607.19126/) (2026)

## Abstract (arXiv)

Score-based 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 a classifier for uncorrupted data is given. We propose a method that, given a pre-trained unconditional score-based generative model, samples from the conditional distribution under arbitrary logical constraints, without requiring additional training. Differently from other zero-shot techniques, that rather aim at generating valid conditional samples, our method is designed for approximating the true conditional distribution. 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 in approximating conditional distributions for various types of constraints and data: tabular data, images and time series.