# Deep Data Consistency: a Fast and Robust Diffusion Model-based Solver for Inverse Problems

arXiv: https://arxiv.org/abs/2405.10748 · HTML: https://mlsanity.com/paper/2405.10748/

## Key facts

- Cited by 4 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 29 of its 42 references that are in the map.
- First posted on arXiv 17 May 2024.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [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)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (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)
- [Direct Diffusion Bridge using Data Consistency for Inverse Problems](https://mlsanity.com/paper/2305.19809/) (2023)
- [Explore Image Deblurring via Blur Kernel Space](https://mlsanity.com/paper/2104.00317/) (2021)
- [Tutorial: Deriving the Standard Variational Autoencoder (VAE) Loss Function](https://mlsanity.com/paper/1907.08956/) (2019)
- [On bayesian estimation and proximity operators](https://mlsanity.com/paper/1807.04021/) (2018)
- [Mitigating Data Consistency Induced Discrepancy in Cascaded Diffusion Models for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2403.09355/) (2024)
- [Analysis of Different Losses for Deep Learning Image Colorization](https://mlsanity.com/paper/2204.02980/) (2022)

## Built on by (most cited first, 4 of 4)

- [OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offs](https://mlsanity.com/paper/2412.09465/) (2024)
- [Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolation](https://mlsanity.com/paper/2503.10103/) (2025)
- [DICE: Diffusion Consensus Equilibrium for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2509.14566/) (2025)
- [High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction](https://mlsanity.com/paper/2607.01176/) (2026)

## Abstract (arXiv)

Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix decomposition, or optimization algorithms, but it is hard to balance the data consistency and realness. The slow sampling speed is also a main obstacle to its wide application. To address the challenges, we propose Deep Data Consistency (DDC) to update the data consistency step with a deep learning model when solving inverse problems with diffusion models. By analyzing existing methods, the variational bound training objective is used to maximize the conditional posterior and reduce its impact on the diffusion process. In comparison with state-of-the-art methods in linear and non-linear tasks, DDC demonstrates its outstanding performance of both similarity and realness metrics in generating high-quality solutions with only 5 inference steps in 0.77 seconds on average. In addition, the robustness of DDC is well illustrated in the experiments across datasets, with large noise and the capacity to solve multiple tasks in only one pre-trained model.