# Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior

arXiv: https://arxiv.org/abs/2501.18913 · HTML: https://mlsanity.com/paper/2501.18913/

## Key facts

- Cited by 22 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 36 of its 48 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## 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 36)

- [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)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [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)
- [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)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [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)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)

## Built on by (most cited first, 22 of 22)

- [Harnessing Diffusion-Yielded Score Priors for Image Restoration](https://mlsanity.com/paper/2507.20590/) (2025)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Enhancing Diffusion Model Stability for Image Restoration via Gradient Management](https://mlsanity.com/paper/2507.06656/) (2025)
- [Physics-informed diffusion models in spectral space](https://mlsanity.com/paper/2602.09708/) (2026)
- [DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing](https://mlsanity.com/paper/2511.17038/) (2025)
- [Local MAP Sampling for Diffusion Models](https://mlsanity.com/paper/2510.07343/) (2025)
- [Diffusion models for multivariate subsurface generation and efficient probabilistic inversion](https://mlsanity.com/paper/2507.15809/) (2025)
- [SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problems](https://mlsanity.com/paper/2509.24580/) (2025)
- [PG-ControlNet: A Physics-Guided ControlNet for Generative Spatially Varying Image Deblurring](https://mlsanity.com/paper/2511.21043/) (2025)
- [Guiding Diffusion with Deep Geometric Moments: Balancing Fidelity and Variation](https://mlsanity.com/paper/2505.12486/) (2025)
- [LatentINDIGO: An INN-Guided Latent Diffusion Algorithm for Image Restoration](https://mlsanity.com/paper/2505.12935/) (2025)
- [GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media](https://mlsanity.com/paper/2602.14642/) (2026)
- [Solving a Nonlinear Blind Inverse Problem for Tagged MRI with Physics and Deep Generative Priors](https://mlsanity.com/paper/2603.00882/) (2026)
- [FlatLands: Generative Floormap Completion From a Single Egocentric View](https://mlsanity.com/paper/2603.16016/) (2026)
- [Proximal-Based Generative Modeling for Bayesian Inverse Problems](https://mlsanity.com/paper/2605.13278/) (2026)
- [Stage-wise Distortion-Perception Traversal in Zero-shot Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2605.28711/) (2026)
- [Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems](https://mlsanity.com/paper/2606.22346/) (2026)
- [DICT: Data Injection and Contrastive Trajectory Refinement for Conditional Image Generation with Diffusion Models](https://mlsanity.com/paper/2607.03899/) (2026)
- [Generative Atmospheric Super-Resolution from Heterogeneous In Situ Observations through Composable Interfaces](https://mlsanity.com/paper/2609.29027/) (2026)
- [Livin' on a Prior: Likelihood Score Approximation for Inverse Problems](https://mlsanity.com/paper/2609.34446/) (2026)
- [EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation](https://mlsanity.com/paper/2609.35944/) (2026)
- [Frequency-Decoupled Diffusion Guidance for Non-Blind Image Deblurring](https://mlsanity.com/paper/2610.06221/) (2026)

## Abstract (arXiv)

Recent advancements in diffusion models have been leveraged to address inverse problems without additional training, and Diffusion Posterior Sampling (DPS) (Chung et al., 2022a) is among the most popular approaches. Previous analyses suggest that DPS accomplishes posterior sampling by approximating the conditional score. While in this paper, we demonstrate that the conditional score approximation employed by DPS is not as effective as previously assumed, but rather aligns more closely with the principle of maximizing a posterior (MAP). This assertion is substantiated through an examination of DPS on 512x512 ImageNet images, revealing that: 1) DPS's conditional score estimation significantly diverges from the score of a well-trained conditional diffusion model and is even inferior to the unconditional score; 2) The mean of DPS's conditional score estimation deviates significantly from zero, rendering it an invalid score estimation; 3) DPS generates high-quality samples with significantly lower diversity. In light of the above findings, we posit that DPS more closely resembles MAP than a conditional score estimator, and accordingly propose the following enhancements to DPS: 1) we explicitly maximize the posterior through multi-step gradient ascent and projection; 2) we utilize a light-weighted conditional score estimator trained with only 100 images and 8 GPU hours. Extensive experimental results indicate that these proposed improvements significantly enhance DPS's performance. The source code for these improvements is provided in https://github.com/tongdaxu/Rethinking-Diffusion-Posterior-Sampling-From-Conditional-Score-Estimator-to-Maximizing-a-Posterior.