# Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver

arXiv: https://arxiv.org/abs/2508.02964 · HTML: https://mlsanity.com/paper/2508.02964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 23 of its 55 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [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)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Monte Carlo guided Diffusion for Bayesian linear inverse problems](https://mlsanity.com/paper/2308.07983/) (2023)
- [Provable Probabilistic Imaging using Score-Based Generative Priors](https://mlsanity.com/paper/2310.10835/) (2023)

## Built on by (most cited first, 1 of 1)

- [AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation](https://mlsanity.com/paper/2609.32411/) (2026)

## Abstract (arXiv)

Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula, which relates the diffusion variate xt to the posterior mean mathbbE [x0 | xt], in order to guide the diffusion trajectory with an estimate of the final denoised sample x0. However, this does not consider information from the measurement y, which must then be integrated downstream. In this work, we propose to estimate the conditional posterior mean mathbbE [x0 | xt, y], which can be formulated as the solution to a lightweight, single-parameter maximum likelihood estimation problem. The resulting prediction can be integrated into any standard sampler, resulting in a fast and memory-efficient inverse solver. Our optimizer is amenable to a noise-aware likelihood-based stopping criteria that is robust to measurement noise in y. We demonstrate comparable or improved performance against a wide selection of contemporary inverse solvers across multiple datasets and tasks.