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

TL;DR

This paper introduces a zero-shot method for conditioning score-based diffusion models on arbitrary logical constraints without additional training, enabling flexible conditional sampling across diverse data types.

Contribution

It presents a novel neuro-symbolic framework that manipulates learned scores to approximate true conditional distributions without retraining models.

Findings

Effective in approximating conditional distributions for tabular data, images, and time series.

Does not require additional training or classifier guidance.

Provides a flexible, numerically stable approach for logical constraint encoding.

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.