Improving Diffusion Models for Inverse Problems using Manifold Constraints

• URL: http://arxiv.org/abs/2206.00941v3
• Date: Mon, 20 May 2024 04:05:20 GMT
• Title: Improving Diffusion Models for Inverse Problems using Manifold Constraints
• Authors: Hyungjin Chung, Byeongsu Sim, Dohoon Ryu, Jong Chul Ye,
• Abstract summary: We show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint. We show that our method is superior to the previous methods both theoretically and empirically.
• Score: 55.91148172752894
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Related papers

• Diffusion State-Guided Projected Gradient for Inverse Problems [82.24625224110099]
  We propose Diffusion State-Guided Projected Gradient (DiffStateGrad) for inverse problems. DiffStateGrad projects the measurement gradient onto a subspace that is a low-rank approximation of an intermediate state of the diffusion process. We highlight that DiffStateGrad improves the robustness of diffusion models in terms of the choice of measurement guidance step size and noise.
  arXiv  Detail & Related papers  (2024-10-04T14:26:54Z)
• 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)
• Fast Samplers for Inverse Problems in Iterative Refinement Models [19.099632445326826]
  We propose a plug-and-play framework for constructing efficient samplers for inverse problems. Our method can generate high-quality samples in as few as 5 conditional sampling steps and outperforms competing baselines requiring 20-1000 steps.
  arXiv  Detail & Related papers  (2024-05-27T21:50:16Z)
• Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution [0.0]
  Current methods assume the degradation to be known and provide impressive results in terms of restoration and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the kernel model. Our method alternates between approximating the expected log-likelihood of the problem using samples drawn from a diffusion model and a step to estimate unknown model parameters.
  arXiv  Detail & Related papers  (2023-09-01T06:47:13Z)
• 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)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems [64.29491112653905]
  We propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods. Specifically, we prove that if tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG with the denoised data ensures the data consistency update to remain in the tangent space. Our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method.
  arXiv  Detail & Related papers  (2023-03-10T07:42:49Z)
• Diffusion Posterior Sampling for General Noisy Inverse Problems [50.873313752797124]
  We extend diffusion solvers to handle noisy (non)linear inverse problems via approximation of the posterior sampling. Our method demonstrates that diffusion models can incorporate various measurement noise statistics.
  arXiv  Detail & Related papers  (2022-09-29T11:12:27Z)

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.