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

2023-08-31

AI Summary

This work addresses the challenge of zero-shot conditional generation from pretrained unconditional diffusion models—specifically, generating samples satisfying complex logical constraints (e.g., structural conditions on tables, images, or time series) without fine-tuning. We propose a neural-symbolic soft-constraint embedding method that encodes first-order logic constraints as differentiable soft penalties and directly perturbs the score function to achieve theoretically consistent approximation of the conditional distribution—bypassing classifier-guided sampling or costly retraining. Our approach integrates score-based modeling, symbolic logic encoding, score correction, and stabilized sampling. Experiments across diverse data modalities demonstrate that our method achieves high-fidelity approximation of the true conditional distribution, significantly outperforming existing zero-shot conditional generation baselines.

Abstract

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.

Problem

• Conditional Generation
• Rating Diffusion Model
• Unsupervised Learning

Innovation

• Condition-aware Generation
• Scoring Diffusion Models
• Adaptive Rule Processing