Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions

• URL: http://arxiv.org/abs/2507.07008v1
• Date: Wed, 09 Jul 2025 16:36:51 GMT
• Title: Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
• Authors: Emile Pierret, Bruno Galerne,
• Abstract summary: We investigate the accuracy of diffusion models when applied to a Gaussian data distribution for deblurring.<n>Within this constrained context, we are able to precisely analyze the discrepancy between the theoretical resolution of inverse problems and their resolution obtained using diffusion models.<n>Our findings allow for the comparison of different algorithms from the literature.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as inpainting, super-resolution, and deblurring. However, several unresolved questions remain about how well they perform. In this article, we investigate the accuracy of these models when applied to a Gaussian data distribution for deblurring. Within this constrained context, we are able to precisely analyze the discrepancy between the theoretical resolution of inverse problems and their resolution obtained using diffusion models by computing the exact Wasserstein distance between the distribution of the diffusion model sampler and the ideal distribution of solutions to the inverse problem. Our findings allow for the comparison of different algorithms from the literature.

Related papers

• EquiReg: Equivariance Regularized Diffusion for Inverse Problems [67.01847869495558]
  We propose EquiReg diffusion, a framework for regularizing posterior sampling in diffusion-based inverse problem solvers.<n>When applied to a variety of solvers, EquiReg outperforms state-of-the-art diffusion models in both linear and nonlinear image restoration tasks.
  arXiv  Detail & Related papers  (2025-05-29T01:25:43Z)
• DIVE: Inverting Conditional Diffusion Models for Discriminative Tasks [79.50756148780928]
  This paper studies the problem of leveraging pretrained diffusion models for performing discriminative tasks.<n>We extend the discriminative capability of pretrained frozen generative diffusion models from the classification task to the more complex object detection task, by "inverting" a pretrained layout-to-image diffusion model.
  arXiv  Detail & Related papers  (2025-04-24T05:13:27Z)
• A Mixture-Based Framework for Guiding Diffusion Models [19.83064246586143]
  Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems.<n>Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems.<n>This work proposes a novel mixture approximation of these intermediate distributions.
  arXiv  Detail & Related papers  (2025-02-05T16:26:06Z)
• 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)
• Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors [0.0]
  We study the behavior of diffusion models and their numerical implementation when the data distribution is Gaussian.<n>We compute the exact Wasserstein errors between the target and the numerically sampled distributions for any numerical scheme.
  arXiv  Detail & Related papers  (2024-05-23T07:28:56Z)
• 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.<n>We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods.<n>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)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• 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)
• Denoising Diffusion Samplers [41.796349001299156]
  Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. We explore a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling.
  arXiv  Detail & Related papers  (2023-02-27T14:37:16Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• Resampling Base Distributions of Normalizing Flows [0.0]
  We introduce a base distribution for normalizing flows based on learned rejection sampling. We develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the reverse Kullback-Leibler divergence.
  arXiv  Detail & Related papers  (2021-10-29T14:44:44Z)

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.