# How Good Are Deep Generative Models for Solving Inverse Problems?

arXiv: https://arxiv.org/abs/2312.12691 · HTML: https://mlsanity.com/paper/2312.12691/

## 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 24 of its 27 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Toward Multimodal Image-to-Image Translation](https://mlsanity.com/paper/1711.11586/) (2017)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Mode Seeking Generative Adversarial Networks for Diverse Image Synthesis](https://mlsanity.com/paper/1903.05628/) (2019)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/1809.09087/) (2018)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [QS-Attn: Query-Selected Attention for Contrastive Learning in I2I Translation](https://mlsanity.com/paper/2203.08483/) (2022)
- [DivCo: Diverse Conditional Image Synthesis via Contrastive Generative Adversarial Network](https://mlsanity.com/paper/2103.07893/) (2021)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Conffusion: Confidence Intervals for Diffusion Models](https://mlsanity.com/paper/2211.09795/) (2022)
- [Image Colorization: A Survey and Dataset](https://mlsanity.com/paper/2008.10774/) (2020)
- [Modulated Contrast for Versatile Image Synthesis](https://mlsanity.com/paper/2203.09333/) (2022)
- [Non-Uniform Diffusion Models](https://mlsanity.com/paper/2207.09786/) (2022)
- [Multimodal Image Synthesis with Conditional Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2004.03590/) (2020)
- [Fast k-Nearest Neighbour Search via Dynamic Continuous Indexing](https://mlsanity.com/paper/1512.00442/) (2015)
- [Fast k-Nearest Neighbour Search via Prioritized DCI](https://mlsanity.com/paper/1703.00440/) (2017)
- [CHIMLE: Conditional Hierarchical IMLE for Multimodal Conditional Image Synthesis](https://mlsanity.com/paper/2211.14286/) (2022)

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

- [A Non-Adversarial Approach to Idempotent Generative Modelling](https://mlsanity.com/paper/2511.02614/) (2025)

## Abstract (arXiv)

Deep generative models, such as diffusion models, GANs, and IMLE, have shown impressive capability in tackling inverse problems. However, the validity of model-generated solutions w.r.t. the forward problem and the reliability of associated uncertainty estimates remain understudied. This study evaluates recent diffusion-based, GAN-based, and IMLE-based methods on three inverse problems, i.e., 16× super-resolution, colourization, and image decompression. We assess the validity of these models' outputs as solutions to the inverse problems and conduct a thorough analysis of the reliability of the models' estimates of uncertainty over the solution. Overall, we find that the IMLE-based CHIMLE method outperforms other methods in terms of producing valid solutions and reliable uncertainty estimates.