Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems

• URL: http://arxiv.org/abs/2303.05754v3
• Date: Mon, 19 Feb 2024 14:34:59 GMT
• Title: Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems
• Authors: Hyungjin Chung, Suhyeon Lee, Jong Chul Ye
• Abstract summary: 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.
• Score: 64.29491112653905
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge quickly for large linear inverse problems. For example, the conjugate gradient method (CG), one of the most popular Krylov subspace methods, is based on the idea of minimizing the residual error in the Krylov subspace. However, with the recent advancement of high-performance diffusion solvers for inverse problems, it is not clear how classical wisdom can be synergistically combined with modern diffusion models. In this study, we propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods. Specifically, we prove that if the tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG initialized with the denoised data ensures the data consistency update to remain in the tangent space. This negates the need to compute the manifold-constrained gradient (MCG), leading to a more efficient diffusion sampling method. Our method is applicable regardless of the parametrization and setting (i.e., VE, VP). Notably, we achieve state-of-the-art reconstruction quality on challenging real-world medical inverse imaging problems, including multi-coil MRI reconstruction and 3D CT reconstruction. Moreover, our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method. Code is available at https://github.com/HJ-harry/DDS

Related papers

• Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstruction [13.418240070456987]
  Sub-DM is a subspace diffusion model that restricts the diffusion process via projections onto subspace as the k-space data distribution evolves toward noise. It circumvents the inference challenges posed by the com-plex and high-dimensional characteristics of k-space data. It allows the diffusion processes in different spaces to refine models through a mutual feedback mechanism, enabling the learning of ac-curate prior even when dealing with complex k-space data.
  arXiv  Detail & Related papers  (2024-11-06T08:33:07Z)
• 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)
• Unsupervised Discovery of Interpretable Directions in h-space of Pre-trained Diffusion Models [63.1637853118899]
  We propose the first unsupervised and learning-based method to identify interpretable directions in h-space of pre-trained diffusion models. We employ a shift control module that works on h-space of pre-trained diffusion models to manipulate a sample into a shifted version of itself. By jointly optimizing them, the model will spontaneously discover disentangled and interpretable directions.
  arXiv  Detail & Related papers  (2023-10-15T18:44:30Z)
• Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography [58.60249163402822]
  Unknown-view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown, random orientations. The proposed OMR is more robust and performs significantly better than the previous state-of-the-art OMR approach.
  arXiv  Detail & Related papers  (2022-07-06T21:40:59Z)
• Improving Diffusion Models for Inverse Problems using Manifold Constraints [55.91148172752894]
  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.
  arXiv  Detail & Related papers  (2022-06-02T09:06:10Z)
• Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction [31.61199061999173]
  Diffusion models have a critical downside - they are inherently slow to sample from, needing few thousand steps of iteration to generate images from pure Gaussian noise. We show that starting from Gaussian noise is unnecessary. Instead, starting from a single forward diffusion with better initialization significantly reduces the number of sampling steps in the reverse conditional diffusion. New sampling strategy, dubbed ComeCloser-DiffuseFaster (CCDF), also reveals a new insight on how the existing feedforward neural network approaches for inverse problems can be synergistically combined with the diffusion models.
  arXiv  Detail & Related papers  (2021-12-09T04:28:41Z)
• Intermediate Layer Optimization for Inverse Problems using Deep Generative Models [86.29330440222199]
  ILO is a novel optimization algorithm for solving inverse problems with deep generative models. We empirically show that our approach outperforms state-of-the-art methods introduced in StyleGAN-2 and PULSE for a wide range of inverse problems.
  arXiv  Detail & Related papers  (2021-02-15T06:52:22Z)

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.