逻辑引导用于扩散模型的精确组合
Logical Guidance for the Exact Composition of Diffusion Models
AI总结：
本文提出LOGDIFF框架，通过逻辑引导实现复杂逻辑表达的精确生成，基于布尔演算和递归算法，适用于图像和蛋白质结构生成。
摘要：
我们提出LOGDIFF（逻辑引导用于扩散模型的精确组合），一种扩散模型的引导框架，使在推理时能通过复杂逻辑表达式实现原理性的约束生成。我们研究何时能从与原子属性相关的引导信号中获得复杂逻辑公式的精确分数引导。首先，我们推导出一个精确的布尔演算，提供精确逻辑引导的充分条件。具体而言，如果一个公式允许一个电路表示，其中合取连接条件独立的子公式，而析取连接条件独立或互斥的子公式，则可实现精确逻辑引导。在这种情况下，引导信号可以通过原子分数和后验概率使用高效的递归算法精确计算。此外，我们证明，对于常见分布类别，任何期望的布尔公式均可编译成此类电路表示。第二，通过将原子引导分数与后验概率估计相结合，我们引入了一种混合引导方法，连接分类器引导和无分类器引导，适用于组合逻辑引导和标准条件生成。我们在多个图像和蛋白质结构生成任务中展示了框架的有效性。
英文摘要：
We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas can be obtained from guidance signals associated with atomic properties. First, we derive an exact Boolean calculus that provides a sufficient condition for exact logical guidance. Specifically, if a formula admits a circuit representation in which conjunctions combine conditionally independent subformulas and disjunctions combine subformulas that are either conditionally independent or mutually exclusive, exact logical guidance is achievable. In this case, the guidance signal can be computed exactly from atomic scores and posterior probabilities using an efficient recursive algorithm. Moreover, we show that, for commonly encountered classes of distributions, any desired Boolean formula is compilable into such a circuit representation. Second, by combining atomic guidance scores with posterior probability estimates, we introduce a hybrid guidance approach that bridges classifier guidance and classifier-free guidance, applicable to both compositional logical guidance and standard conditional generation. We demonstrate the effectiveness of our framework on multiple image and protein structure generation tasks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
