# Conditional Mutual Information Based Diffusion Posterior Sampling for Solving Inverse Problems

arXiv: https://arxiv.org/abs/2501.02880 · HTML: https://mlsanity.com/paper/2501.02880/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 6 Jan 2025.

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance](https://mlsanity.com/paper/2402.02149/) (2024)
- [Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling](https://mlsanity.com/paper/2412.20045/) (2024)

## Built on by (most cited first, 3 of 3)

- [Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling](https://mlsanity.com/paper/2510.09676/) (2025)
- [Posterior Information Dynamics of Diffusion Models for Linear Inverse Problems](https://mlsanity.com/paper/2608.21709/) (2026)
- [Opening the Black Box of Classifier-Free Guidance via Information Bottleneck](https://mlsanity.com/paper/2610.13369/) (2026)

## Abstract (arXiv)

Inverse problems are prevalent across various disciplines in science and engineering. In the field of computer vision, tasks such as inpainting, deblurring, and super-resolution are commonly formulated as inverse problems. Recently, diffusion models (DMs) have emerged as a promising approach for addressing noisy linear inverse problems, offering effective solutions without requiring additional task-specific training. Specifically, with the prior provided by DMs, one can sample from the posterior by finding the likelihood. Since the likelihood is intractable, it is often approximated in the literature. However, this approximation compromises the quality of the generated images. To overcome this limitation and improve the effectiveness of DMs in solving inverse problems, we propose an information-theoretic approach. Specifically, we maximize the conditional mutual information I(boldsymbolx0; boldsymboly | boldsymbolxt), where boldsymbolx0 represents the reconstructed signal, boldsymboly is the measurement, and boldsymbolxt is the intermediate signal at stage t. This ensures that the intermediate signals boldsymbolxt are generated in a way that the final reconstructed signal boldsymbolx0 retains as much information as possible about the measurement boldsymboly. We demonstrate that this method can be seamlessly integrated with recent approaches and, once incorporated, enhances their performance both qualitatively and quantitatively.