Interpretable Diffusion via Information Decomposition
This work addresses the interpretability challenge in diffusion models for researchers and practitioners, offering a novel method to analyze and control model behavior, though it is incremental in applying information theory to an existing framework.
The paper tackles the problem of interpreting the relationships learned by diffusion models, such as those between words and image parts, by establishing a connection between diffusion and information decomposition, enabling quantification of specific relationships and applications like unsupervised object localization and image editing.
Denoising diffusion models enable conditional generation and density modeling of complex relationships like images and text. However, the nature of the learned relationships is opaque making it difficult to understand precisely what relationships between words and parts of an image are captured, or to predict the effect of an intervention. We illuminate the fine-grained relationships learned by diffusion models by noticing a precise relationship between diffusion and information decomposition. Exact expressions for mutual information and conditional mutual information can be written in terms of the denoising model. Furthermore, pointwise estimates can be easily estimated as well, allowing us to ask questions about the relationships between specific images and captions. Decomposing information even further to understand which variables in a high-dimensional space carry information is a long-standing problem. For diffusion models, we show that a natural non-negative decomposition of mutual information emerges, allowing us to quantify informative relationships between words and pixels in an image. We exploit these new relations to measure the compositional understanding of diffusion models, to do unsupervised localization of objects in images, and to measure effects when selectively editing images through prompt interventions.