# Interpretable Diffusion via Information Decomposition

arXiv: https://arxiv.org/abs/2310.07972 · HTML: https://mlsanity.com/paper/2310.07972/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 56 of its 77 references that are in the map.
- First posted on arXiv 12 Oct 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 56)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Open-Vocabulary Panoptic Segmentation with Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.04803/) (2023)
- [Multimodal datasets: misogyny, pornography, and malignant stereotypes](https://mlsanity.com/paper/2110.01963/) (2021)
- [Unleashing Text-to-Image Diffusion Models for Visual Perception](https://mlsanity.com/paper/2303.02153/) (2023)
- [Easily Accessible Text-to-Image Generation Amplifies Demographic Stereotypes at Large Scale](https://mlsanity.com/paper/2211.03759/) (2022)
- [What the DAAM: Interpreting Stable Diffusion Using Cross Attention](https://mlsanity.com/paper/2210.04885/) (2022)

## Built on by (most cited first, 30 of 37)

- [Explainable and Interpretable Multimodal Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2412.02104/) (2024)
- [IsoBench: Benchmarking Multimodal Foundation Models on Isomorphic Representations](https://mlsanity.com/paper/2404.01266/) (2024)
- [Visual Large Language Models for Generalized and Specialized Applications](https://mlsanity.com/paper/2501.02765/) (2025)
- [CPR: Retrieval Augmented Generation for Copyright Protection](https://mlsanity.com/paper/2403.18920/) (2024)
- [Diffusion Attribution Score: Evaluating Training Data Influence in Diffusion Models](https://mlsanity.com/paper/2410.18639/) (2024)
- [Aligning Text to Image in Diffusion Models is Easier Than You Think](https://mlsanity.com/paper/2503.08250/) (2025)
- [Approximating mutual information of high-dimensional variables using learned representations](https://mlsanity.com/paper/2409.02732/) (2024)
- [DiffusionPID: Interpreting Diffusion via Partial Information Decomposition](https://mlsanity.com/paper/2406.05191/) (2024)
- [Entropic Time Schedulers for Generative Diffusion Models](https://mlsanity.com/paper/2504.13612/) (2025)
- [Euclid: Supercharging Multimodal LLMs with Synthetic High-Fidelity Visual Descriptions](https://mlsanity.com/paper/2412.08737/) (2024)
- [The Information Dynamics of Generative Diffusion](https://mlsanity.com/paper/2508.19897/) (2025)
- [Visually Guided Decoding: Gradient-Free Hard Prompt Inversion with Language Models](https://mlsanity.com/paper/2505.08622/) (2025)
- [The Entropic Signature of Class Speciation in Diffusion Models](https://mlsanity.com/paper/2602.09651/) (2026)
- [Information Theoretic Text-to-Image Alignment](https://mlsanity.com/paper/2405.20759/) (2024)
- [Information-Theoretic Proofs for Diffusion Sampling](https://mlsanity.com/paper/2502.02305/) (2025)
- [Your Diffusion Model is Secretly a Noise Classifier and Benefits from Contrastive Training](https://mlsanity.com/paper/2407.08946/) (2024)
- [Interpretable Measures of Conceptual Similarity by Complexity-Constrained Descriptive Auto-Encoding](https://mlsanity.com/paper/2402.08919/) (2024)
- [Generative Distribution Embeddings: Lifting autoencoders to the space of distributions for multiscale representation learning](https://mlsanity.com/paper/2505.18150/) (2025)
- [SOmegaI: Score-based O-INFORMATION Estimation](https://mlsanity.com/paper/2402.05667/) (2024)
- [MMG: Mutual Information Estimation via the MMSE Gap in Diffusion](https://mlsanity.com/paper/2509.20609/) (2025)
- [Information-Theoretic Discrete Diffusion](https://mlsanity.com/paper/2510.24088/) (2025)
- [Learning to Match Unpaired Data with Minimum Entropy Coupling](https://mlsanity.com/paper/2503.08501/) (2025)
- [On the Separability of Information in Diffusion Models](https://mlsanity.com/paper/2509.23937/) (2025)
- [Attention, May I Have Your Decision? Localizing Generative Choices in Diffusion Models](https://mlsanity.com/paper/2604.06052/) (2026)
- [A Neural Difference-of-Entropies Estimator for Mutual Information](https://mlsanity.com/paper/2502.13085/) (2025)
- [InfSplign: Inference-Time Spatial Alignment of Text-to-Image Diffusion Models](https://mlsanity.com/paper/2512.17851/) (2025)
- [Relative Entropy Estimation in Function Space: Theory and Applications to Trajectory Inference](https://mlsanity.com/paper/2604.20775/) (2026)
- [Conjuring Semantic Similarity](https://mlsanity.com/paper/2410.16431/) (2024)
- [Decomposing stimulus-specific sensory neural information via diffusion models](https://mlsanity.com/paper/2505.11309/) (2025)
- [Improving Compositional Generation with Diffusion Models Using Lift Scores](https://mlsanity.com/paper/2505.13740/) (2025)

## Abstract (arXiv)

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.