Conditioning Score-Based Generative Models by Neuro-Symbolic Constraints
Davide Scassola Sebastiano Saccani Ginevra Carbone Luca Bortolussi
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.