# PRISM: Probabilistic and Robust Inverse Solver with Measurement-Conditioned Diffusion Prior for Blind Inverse Problems

arXiv: https://arxiv.org/abs/2509.16106 · HTML: https://mlsanity.com/paper/2509.16106/

## Key facts

- Cited by 2 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 1 of its 23 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Placed in

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

## Builds on (most cited first, 1 of 1)

- [Plug-and-Play Posterior Sampling for Blind Inverse Problems](https://mlsanity.com/paper/2505.22923/) (2025)

## Built on by (most cited first, 2 of 2)

- [Generator-Guided Inverse Sampling for L'evy-Driven Generative Models](https://mlsanity.com/paper/2608.10384/) (2026)
- [FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants](https://mlsanity.com/paper/2609.20769/) (2026)

## Abstract (arXiv)

Diffusion models are now commonly used to solve inverse problems in computational imaging. However, most diffusion-based inverse solvers require complete knowledge of the forward operator to be used. In this work, we introduce a novel probabilistic and robust inverse solver with measurement-conditioned diffusion prior (PRISM) to effectively address blind inverse problems. PRISM offers a technical advancement over current methods by incorporating a powerful measurement-conditioned diffusion model into a theoretically principled posterior sampling scheme. Experiments on blind image deblurring validate the effectiveness of the proposed method, demonstrating the superior performance of PRISM over state-of-the-art baselines in both image and blur kernel recovery.