mlsanityData to 7 Oct 2026

Amortized Posterior Sampling with Diffusion Prior Distillation

arXiv 2407.17907 ↗First posted 25 Jul 2024cs.CV cs.LGcited by 6

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems. Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model. This results in a powerful, amortized sampler capable of generating diverse posterior samples with a single neural function evaluation, generalizing across various measurements. Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains. We demonstrate its effectiveness on a range of tasks, including image restoration, manifold signal reconstruction, and climate data imputation. APS significantly outperforms existing approaches in computational efficiency while maintaining competitive reconstruction quality, enabling real-time, high-quality solutions to inverse problems across diverse domains.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 34 of its 47 references that are in the map. First posted on arXiv 25 Jul 2024.

Builds on

34 of 47 references.

Closest ancestors · 10

Same direction, newest first

  1. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance3 Feb
  2. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  3. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  4. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  5. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems10 Mar
  6. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  7. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  8. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  9. 2022Denoising Diffusion Restoration Models27 Jan
  10. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 24

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  8. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  9. 2015Variational Inference with Normalizing Flowscited by 2,161
  10. 2016Density estimation using Real NVPcited by 2,029
  11. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  12. 2023Consistency Modelscited by 1,778
12 more
  1. 2023ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillationcited by 1,207
  2. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  3. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 232
  4. 2020SRFlow: Learning the Super-Resolution Space with Normalizing Flowcited by 209
  5. 2022From data to functa: Your data point is a function and you can treat it like onecited by 183
  6. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Modelscited by 130
  7. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 110
  8. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 108
  9. 2023BOOT: Data-free Distillation of Denoising Diffusion Models with Bootstrappingcited by 96
  10. 2021Generative Models as Distributions of Functionscited by 89
  11. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  12. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 2.

6 papers.

  1. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 33
  2. 2025Diffusion models for inverse problemscited by 15
  3. 2026Variational Flow Maps: Make Some Noise for One-Step Conditional Generationcited by 5
  4. 2025EquiReg: Equivariance Regularized Diffusion for Inverse Problemscited by 1
  5. 2025Noise Conditional Variational Score Distillationcited by 1
  6. 2026Exact Posterior Score Estimation for Solving Linear Inverse Problemscited by 1

Similar, not cited

Close in wording, no citation either way

  1. 2024Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems
  2. 2026Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inference
  3. 2026U-DAVI: Uncertainty-Aware Diffusion-Prior-Based Amortized Variational Inference for Image Reconstruction
  4. 2026Discrete Langevin-Inspired Posterior Sampling
  5. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  6. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  7. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  8. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models