# Generative diffusion posterior sampling for informative likelihoods

arXiv: https://arxiv.org/abs/2506.01083 · HTML: https://mlsanity.com/paper/2506.01083/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 16 of 16)

- [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)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [From Denoising Diffusions to Denoising Markov Models](https://mlsanity.com/paper/2211.03595/) (2022)
- [Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors](https://mlsanity.com/paper/2403.11407/) (2024)
- [Conditional sampling within generative diffusion models](https://mlsanity.com/paper/2409.09650/) (2024)
- [Taming Diffusion Models for Image Restoration: A Review](https://mlsanity.com/paper/2409.10353/) (2024)
- [Conditioning diffusion models by explicit forward-backward bridging](https://mlsanity.com/paper/2405.13794/) (2024)
- [Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo](https://mlsanity.com/paper/2502.06379/) (2025)
- [Reverse Markov Learning: Multi-Step Generative Models for Complex Distributions](https://mlsanity.com/paper/2502.13747/) (2025)

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

- [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)
- [Diffusion differentiable resampling](https://mlsanity.com/paper/2512.10401/) (2025)
- [Particle-Guided Diffusion for Gas-Phase Reaction Kinetics](https://mlsanity.com/paper/2603.05139/) (2026)

## Abstract (arXiv)

Sequential Monte Carlo (SMC) methods have recently shown successful results for conditional sampling of generative diffusion models. In this paper we propose a new diffusion posterior SMC sampler achieving improved statistical efficiencies, particularly under outlier conditions or highly informative likelihoods. The key idea is to construct an observation path that correlates with the diffusion model and to design the sampler to leverage this correlation for more efficient sampling. Empirical results conclude the efficiency.