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.

提出了一种从条件的基于分数的生成模型中强制执行任意逻辑约束条件进行采样的方法，采用柔性和数值稳定的神经符号框架来编码逻辑约束条件，并通过有效的启发式算法改进了近似条件采样算法的准确性。