# A Mixture-Based Framework for Guiding Diffusion Models

arXiv: https://arxiv.org/abs/2502.03332 · HTML: https://mlsanity.com/paper/2502.03332/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- First posted on arXiv 5 Feb 2025.

## Placed in

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

## Built on by (most cited first, 18 of 18)

- [Solving Inverse Problems with FLAIR](https://mlsanity.com/paper/2506.02680/) (2025)
- [Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2505.20789/) (2025)
- [Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors](https://mlsanity.com/paper/2510.10968/) (2025)
- [Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidance](https://mlsanity.com/paper/2512.18365/) (2025)
- [Particle-Guided Diffusion Models for Partial Differential Equations](https://mlsanity.com/paper/2601.23262/) (2026)
- [Local MAP Sampling for Diffusion Models](https://mlsanity.com/paper/2510.07343/) (2025)
- [Image Restoration via Diffusion Models with Dynamic Resolution](https://mlsanity.com/paper/2605.14267/) (2026)
- [Stein Diffusion Guidance: Training-Free Posterior Correction for Sampling Beyond High-Density Regions](https://mlsanity.com/paper/2507.05482/) (2025)
- [SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problems](https://mlsanity.com/paper/2509.24580/) (2025)
- [Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inference](https://mlsanity.com/paper/2602.07102/) (2026)
- [Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey](https://mlsanity.com/paper/2510.14114/) (2025)
- [Model-free filtering in high dimensions via projection and score-based diffusions](https://mlsanity.com/paper/2510.23197/) (2025)
- [When Test-Time Guidance Is Enough: Fast Image and Video Editing with Diffusion Guidance](https://mlsanity.com/paper/2602.14157/) (2026)
- [Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors](https://mlsanity.com/paper/2605.05520/) (2026)
- [SURF: Separation via Unsupervised Remixing Flow](https://mlsanity.com/paper/2606.04921/) (2026)
- [Direct Conditional Transition Sampling for Diffusion Inverse Problems](https://mlsanity.com/paper/2609.14596/) (2026)
- [Backward SDEs-based Diffusion for Physics-Constrained Generation](https://mlsanity.com/paper/2609.15702/) (2026)
- [Mixed Poisson diffusion models and application to posterior sampling](https://mlsanity.com/paper/2610.20218/) (2026)

## Abstract (arXiv)

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time compute and thereby eliminating the need to retrain task-specific models on the same dataset. To approximate the posterior of a Bayesian inverse problem, a diffusion model samples from a sequence of intermediate posterior distributions, each with an intractable likelihood function. This work proposes a novel mixture approximation of these intermediate distributions. Since direct gradient-based sampling of these mixtures is infeasible due to intractable terms, we propose a practical method based on Gibbs sampling. We validate our approach through extensive experiments on image inverse problems, utilizing both pixel- and latent-space diffusion priors, as well as on source separation with an audio diffusion model. The code is available at https://www.github.com/badr-moufad/mgdm