# Diffusion Models for Inverse Problems in the Exponential Family

arXiv: https://arxiv.org/abs/2502.05994 · HTML: https://mlsanity.com/paper/2502.05994/

## 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 14 of its 35 references that are in the map.
- First posted on arXiv 9 Feb 2025.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Compositional Score Modeling for Simulation-based Inference](https://mlsanity.com/paper/2209.14249/) (2022)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Improved prediction accuracy for disease risk mapping using Gaussian Process stacked generalisation](https://mlsanity.com/paper/1612.03278/) (2016)

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

- [Eval4DiRec: A Unified and Systematic Evaluation Framework for Diffusion-based Recommender Systems](https://mlsanity.com/paper/2609.34404/) (2026)

## Abstract (arXiv)

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due to the intractability of the likelihood score, which until now has only been approximated in the simpler case of Gaussian likelihoods. In this work, we extend diffusion models to handle inverse problems where the observations follow a distribution from the exponential family, such as a Poisson or a Binomial distribution. By leveraging the conjugacy properties of exponential family distributions, we introduce the evidence trick, a method that provides a tractable approximation to the likelihood score. In our experiments, we demonstrate that our methodology effectively performs Bayesian inference on spatially inhomogeneous Poisson processes with intensities as intricate as ImageNet images. Furthermore, we demonstrate the real-world impact of our methodology by showing that it performs competitively with the current state-of-the-art in predicting malaria prevalence estimates in Sub-Saharan Africa.