# Score-Based Variational Inference for Inverse Problems

arXiv: https://arxiv.org/abs/2410.05646 · HTML: https://mlsanity.com/paper/2410.05646/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Robust Compressed Sensing using Generative Models](https://mlsanity.com/paper/2006.09461/) (2020)

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

- [Traversing Distortion-Perception Tradeoff using a Single Score-Based Generative Model](https://mlsanity.com/paper/2503.20297/) (2025)
- [Stage-wise Distortion-Perception Traversal in Zero-shot Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2605.28711/) (2026)

## Abstract (arXiv)

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple samples from the posterior which is time-consuming. In this work, by analyzing the probability density evolution of the conditional reverse diffusion process, we prove that the posterior mean can be achieved by tracking the mean of each reverse diffusion step. Based on that, we establish a framework termed reverse mean propagation (RMP) that targets the posterior mean directly. We show that RMP can be implemented by solving a variational inference problem, which can be further decomposed as minimizing a reverse KL divergence at each reverse step. We further develop an algorithm that optimizes the reverse KL divergence with natural gradient descent using score functions and propagates the mean at each reverse step. Experiments demonstrate the validity of the theory of our framework and show that our algorithm outperforms state-of-the-art algorithms on reconstruction performance with lower computational complexity in various inverse problems.