# SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems

arXiv: https://arxiv.org/abs/2410.04479 · HTML: https://mlsanity.com/paper/2410.04479/

## Key facts

- Cited by 24 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 38 of its 56 references that are in the map.
- First posted on arXiv 6 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [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)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [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)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)
- [DiffiT: Diffusion Vision Transformers for Image Generation](https://mlsanity.com/paper/2312.02139/) (2023)

## Built on by (most cited first, 24 of 24)

- [OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offs](https://mlsanity.com/paper/2412.09465/) (2024)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [UGoDIT: Unsupervised Group Deep Image Prior Via Transferable Weights](https://mlsanity.com/paper/2505.11720/) (2025)
- [EquiReg: Equivariance Regularized Diffusion for Inverse Problems](https://mlsanity.com/paper/2505.22973/) (2025)
- [Benchmarking Diffusion Annealing-Based Bayesian Inverse Problem Solvers](https://mlsanity.com/paper/2503.03007/) (2025)
- [Local MAP Sampling for Diffusion Models](https://mlsanity.com/paper/2510.07343/) (2025)
- [Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving](https://mlsanity.com/paper/2511.06138/) (2025)
- [Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning](https://mlsanity.com/paper/2604.16919/) (2026)
- [Beyond MMSE: Enhancing PnP Restoration with ProxiMAP](https://mlsanity.com/paper/2605.16396/) (2026)
- [Measurement-Aligned Sampling for Inverse Problem](https://mlsanity.com/paper/2506.11893/) (2025)
- [Generative AI Meets 6G and Beyond: Diffusion Models for Semantic Communications](https://mlsanity.com/paper/2511.08416/) (2025)
- [Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers](https://mlsanity.com/paper/2601.04791/) (2026)
- [FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems](https://mlsanity.com/paper/2603.01591/) (2026)
- [What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View](https://mlsanity.com/paper/2606.24516/) (2026)
- [Improving Decoupled Posterior Sampling for Inverse Problems using Data Consistency Constraint](https://mlsanity.com/paper/2412.00664/) (2024)
- [NERD: Network-Regularized Diffusion Sampling For 3D Computed Tomography](https://mlsanity.com/paper/2511.14680/) (2025)
- [Tada-DIP: Input-adaptive Deep Image Prior for One-shot 3D Image Reconstruction](https://mlsanity.com/paper/2512.03962/) (2025)
- [Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction](https://mlsanity.com/paper/2602.23214/) (2026)
- [Proximal-Based Generative Modeling for Bayesian Inverse Problems](https://mlsanity.com/paper/2605.13278/) (2026)
- [Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping](https://mlsanity.com/paper/2605.27990/) (2026)
- [Stage-wise Distortion-Perception Traversal in Zero-shot Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2605.28711/) (2026)
- [Trajectory Constraints for Imaging Inverse Problems](https://mlsanity.com/paper/2605.29012/) (2026)
- [DICT: Data Injection and Contrastive Trajectory Refinement for Conditional Image Generation with Diffusion Models](https://mlsanity.com/paper/2607.03899/) (2026)
- [Backward SDEs-based Diffusion for Physics-Constrained Generation](https://mlsanity.com/paper/2609.15702/) (2026)

## Abstract (arXiv)

Diffusion models (DMs) are a class of generative models that allow sampling from a distribution learned over a training set. When applied to solving inverse problems, the reverse sampling steps are modified to approximately sample from a measurement-conditioned distribution. However, these modifications may be unsuitable for certain settings (e.g., presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier steps and generally require a large number of optimization and/or sampling steps. To address these challenges, we state three conditions for achieving measurement-consistent diffusion trajectories. Building on these conditions, we propose a new optimization-based sampling method that not only enforces standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates our proposed step-wise and network-regularized backward diffusion consistency that maintains a diffusion trajectory by optimizing over the input of the pre-trained model at every sampling step. By enforcing these conditions (implicitly or explicitly), our sampler requires significantly fewer reverse steps. Therefore, we refer to our method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to SOTA baselines, our experiments across several linear and non-linear tasks (with natural and medical images) demonstrate that SITCOM achieves competitive or superior results in terms of standard similarity metrics and run-time.