Amortized Posterior Sampling with Diffusion Prior Distillation

• URL: http://arxiv.org/abs/2407.17907v2
• Date: Fri, 11 Jul 2025 04:01:19 GMT
• Title: Amortized Posterior Sampling with Diffusion Prior Distillation
• Authors: Abbas Mammadov, Hyungjin Chung, Jong Chul Ye,
• Abstract summary: Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>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.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
• Score: 55.03585818289934
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

Related papers

• Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance [52.705112811734566]
  A novel diffusion-based framework is introduced for solving inverse problems using a piecewise guidance scheme.<n>The proposed method is problem-agnostic and readily adaptable to a variety of inverse problems.<n>The framework achieves a reduction in inference time of (25%) for inpainting with both random and center masks, and (23%) and (24%) for (4times) and (8times) super-resolution tasks.
  arXiv  Detail & Related papers  (2025-07-22T19:35:14Z)
• Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach [19.860268382547357]
  Current DM-based posterior sampling methods rely on approximations to the generative process.<n>We propose an ensemble-based algorithm that performs posterior sampling without the use of approximations.<n>Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo method.
  arXiv  Detail & Related papers  (2025-06-04T14:09:25Z)
• A Mixture-Based Framework for Guiding Diffusion Models [19.83064246586143]
  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. This work proposes a novel mixture approximation of these intermediate distributions.
  arXiv  Detail & Related papers  (2025-02-05T16:26:06Z)
• Geophysical inverse problems with measurement-guided diffusion models [0.4532517021515834]
  I consider two sampling algorithms recently proposed under the name of Diffusion Posterior Sampling (DPS) and Pseudo-inverse Guided Diffusion Model (PGDM)<n>In DPS, the guidance term is obtained by applying the adjoint of the modeling operator to the residual obtained from a one-step denoising estimate of the solution.<n>On the other hand, PGDM utilizes a pseudo-inverse operator that originates from the fact that the one-step denoised solution is not assumed to be deterministic.
  arXiv  Detail & Related papers  (2025-01-08T23:33:50Z)
• Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling [3.866047645663101]
  In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems.<n>DDPMs are shown to provide a promising solution to noisy linear inverse problems without the need for additional task specific training.
  arXiv  Detail & Related papers  (2024-12-28T06:17:44Z)
• Arbitrary-steps Image Super-resolution via Diffusion Inversion [68.78628844966019]
  This study presents a new image super-resolution (SR) technique based on diffusion inversion, aiming at harnessing the rich image priors encapsulated in large pre-trained diffusion models to improve SR performance. We design a Partial noise Prediction strategy to construct an intermediate state of the diffusion model, which serves as the starting sampling point. Once trained, this noise predictor can be used to initialize the sampling process partially along the diffusion trajectory, generating the desirable high-resolution result.
  arXiv  Detail & Related papers  (2024-12-12T07:24:13Z)
• Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements [45.70011319850862]
  Diffusion models have emerged as a powerful foundation model for visual generation. Current posterior sampling based methods take the measurement into the posterior sampling to infer the distribution of the target data. We show that high-frequency information can be prematurely introduced during the early stages, which could induce larger posterior estimate errors. We propose a novel diffusion posterior sampling method DPS-CM, which incorporates a Crafted Measurement.
  arXiv  Detail & Related papers  (2024-11-15T00:06:57Z)
• G2D2: Gradient-guided Discrete Diffusion for image inverse problem solving [55.185588994883226]
  This paper presents a novel method for addressing linear inverse problems by leveraging image-generation models based on discrete diffusion as priors. To the best of our knowledge, this is the first approach to use discrete diffusion model-based priors for solving image inverse problems.
  arXiv  Detail & Related papers  (2024-10-09T06:18:25Z)
• Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling [16.683393726483978]
  Diffusion models can generate a variety of high-quality images by modeling complex data distributions.<n>Most of the existing diffusion-based methods integrate data consistency steps by approximating the likelihood function within the diffusion reverse sampling process.<n>In this paper, we show that the existing approximations are either insufficient or computationally inefficient.
  arXiv  Detail & Related papers  (2024-09-13T15:20:03Z)
• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems [12.482127049881026]
  We propose a novel approach to solve inverse problems with a diffusion prior from an amortized variational inference perspective. Our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements.
  arXiv  Detail & Related papers  (2024-07-23T02:14:18Z)
• New algorithms for sampling and diffusion models [0.0]
  We introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the concept of the reverse diffusion process, widely adopted in diffusion generative models.
  arXiv  Detail & Related papers  (2024-06-14T02:30:04Z)
• Improved off-policy training of diffusion samplers [93.66433483772055]
  We study the problem of training diffusion models to sample from a distribution with an unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods. Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work.
  arXiv  Detail & Related papers  (2024-02-07T18:51:49Z)
• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• A Variational Perspective on Solving Inverse Problems with Diffusion Models [101.831766524264]
  Inverse tasks can be formulated as inferring a posterior distribution over data. This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. We propose a variational approach that by design seeks to approximate the true posterior distribution.
  arXiv  Detail & Related papers  (2023-05-07T23:00:47Z)
• An optimal control perspective on diffusion-based generative modeling [9.806130366152194]
  We establish a connection between optimal control and generative models based on differential equations (SDEs) In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. We develop a novel diffusion-based method for sampling from unnormalized densities.
  arXiv  Detail & Related papers  (2022-11-02T17:59:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.