Interpretable Diffusion via Information Decomposition (2310.07972v3)

Abstract: 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.

• The paper presents a novel framework for information decomposition that quantifies contributions at both pixel and word levels.
• It demonstrates robust compositional understanding by localizing textual cues within generated images, outperforming traditional contrastive models.
• The paper evaluates prompt interventions using Conditional Mutual Information, providing actionable insights for enhancing model interpretability.

Interpretable Diffusion via Information Decomposition

The paper "Interpretable Diffusion via Information Decomposition" introduces a novel approach to understanding the inner workings of denoising diffusion models, widely recognized for their prowess in image and text generation. The central contribution lies in elucidating the relationships that diffusion models learn between images and descriptions, achieved through an information-theoretic perspective. The authors demonstrate an efficient methodology to decompose information, attributing it to individual text and image components, offering insights into the model's understanding and potential interventions.

Key Contributions

1. Information Decomposition: The authors establish a framework where denoising diffusion models are leveraged for fine-grained information decomposition. This decomposition allows precise quantification at the per-sample and per-variable level, offering detailed insights into the informational contributions of pixels and words.
2. Compositional Understanding: In examining diffusion models’ understanding of compositional relationships between images and captions, the paper utilizes the ARO benchmark. The results exhibit that diffusion models, often underestimated, reveal enhanced compositional abilities compared to the commonly used contrastive models like OpenCLIP.
3. Localization of Textual Information: A further analysis addresses how specific words within a text prompt are localized within the resulting image. This exploration underscores the capabilities of diffusion models to recognize and align abstract concepts such as adjectives and verbs more effectively than traditional attention maps.
4. Evaluating Interventions: The paper undertakes a novel examination of how prompt interventions—specifically, word omissions or swaps—affect image generation. The Conditional Mutual Information (CMI) estimates outperform attention-based methodologies in predicting the impact of such interventions, thus providing a quantitative measure of word importance in a given context.

Methodology

The paper builds its methodology on diffusion models as noisy channels, drawing on information theory principles to analyze how information is encoded and processed. By defining optimal denoisers through the lens of Minimum Mean Square Error (MMSE), it interprets these models as approximations of ideal information decomposers. The application of this theoretical framework extends to both Mutual Information (MI) and Conditional Mutual Information (CMI) estimations, setting the foundations for robust analytical computations.

Results and Implications

The experimental outcomes assert that the information decomposition approach clarifies and enhances the interpretability of generative models, moving beyond the constraints of architecture-specific attention mechanisms. The numerical findings on the ARO benchmark, for instance, challenge existing underestimations of diffusion models, advocating for their integration into discriminative tasks traditionally dominated by attention-based frameworks.

The implications of these findings extend beyond conventional generative applications. The ability to pinpoint informative relationships holds potential in diverse sectors such as biotechnology, where identifying gene expression patterns is critical. Additionally, the insights into compositional understanding offer valuable guidance for enhancing other AI models in handling complex relational data.

Future Directions

This paper opens avenues for further exploration of diffusion models' capabilities. Future research could explore mechanistic interpretability to identify neural circuits responsible for specific tasks within diffusion models. Evaluating these models across different domains, particularly those requiring sensitive and accurate data interpretation, could expand the utility of information-theoretic diffusion approaches. Furthermore, incorporating these insights into improving ethical and transparent AI systems remains a pertinent and promising field of inquiry.

In summary, the paper provides a comprehensive framework for understanding and utilizing the intricate relationships modeled by denoising diffusion models, emphasizing the significance of information-theoretic methods in advancing the interpretability and application of complex AI systems.