DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems

• URL: http://arxiv.org/abs/2412.04766v2
• Date: Wed, 12 Mar 2025 17:30:41 GMT
• Title: DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems
• Authors: Shadab Ahamed, Eldad Haber,
• Abstract summary: Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging.<n>We employ Flow Matching (FM), a generative framework that integrates a deterministic processes to map a simple reference distribution.<n>Our method DAWN-FM: Data-AWare and Noise-informed Flow Matching incorporates data and noise embedding, allowing the model to access representations about the measured data.
• Score: 4.212663349859165
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization techniques to stabilize the solution. In this work, we employ Flow Matching (FM), a generative framework that integrates a deterministic processes to map a simple reference distribution, such as a Gaussian, to the target distribution. Our method DAWN-FM: Data-AWare and Noise-informed Flow Matching incorporates data and noise embedding, allowing the model to access representations about the measured data explicitly and also account for noise in the observations, making it particularly robust in scenarios where data is noisy or incomplete. By learning a time-dependent velocity field, FM not only provides accurate solutions but also enables uncertainty quantification by generating multiple plausible outcomes. Unlike pre-trained diffusion models, which may struggle in highly ill-posed settings, our approach is trained specifically for each inverse problem and adapts to varying noise levels. We validate the effectiveness and robustness of our method through extensive numerical experiments on tasks such as image deblurring and tomography.

Related papers

• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations [1.371691382573869]
  We develop and enhance score-based diffusion models in field reconstruction tasks. We introduce a condition encoding approach to construct a tractable mapping mapping between observed and unobserved regions. We demonstrate the ability of the model to capture possible reconstructions and improve the accuracy of fused results.
  arXiv  Detail & Related papers  (2024-08-30T19:46:23Z)
• A quasi-Bayesian sequential approach to deconvolution density estimation [7.10052009802944]
  Density deconvolution addresses the estimation of the unknown density function $f$ of a random signal from data. We consider the problem of density deconvolution in a streaming or online setting where noisy data arrive progressively. By relying on a quasi-Bayesian sequential approach, we obtain estimates of $f$ that are of easy evaluation.
  arXiv  Detail & Related papers  (2024-08-26T16:40:04Z)
• Bayesian Inference of General Noise Model Parameters from Surface Code's Syndrome Statistics [0.0]
  We propose general noise model Bayesian inference methods that integrate the surface code's tensor network simulator. For stationary noise, where the noise parameters are constant and do not change, we propose a method based on the Markov chain Monte Carlo. For time-varying noise, which is a more realistic situation, we introduce another method based on the sequential Monte Carlo.
  arXiv  Detail & Related papers  (2024-06-13T10:26:04Z)
• Blue noise for diffusion models [50.99852321110366]
  We introduce a novel and general class of diffusion models taking correlated noise within and across images into account. Our framework allows introducing correlation across images within a single mini-batch to improve gradient flow. We perform both qualitative and quantitative evaluations on a variety of datasets using our method.
  arXiv  Detail & Related papers  (2024-02-07T14:59:25Z)
• Towards stable real-world equation discovery with assessing differentiating quality influence [52.2980614912553]
  We propose alternatives to the commonly used finite differences-based method. We evaluate these methods in terms of applicability to problems, similar to the real ones, and their ability to ensure the convergence of equation discovery algorithms.
  arXiv  Detail & Related papers  (2023-11-09T23:32:06Z)
• Score-based Diffusion Models in Function Space [140.792362459734]
  Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion [2.2849153854336763]
  temporal data can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the process that governs it. We propose a solution by defining the denoising diffusion model in the function space.
  arXiv  Detail & Related papers  (2022-11-04T17:02:01Z)
• Markup-to-Image Diffusion Models with Scheduled Sampling [111.30188533324954]
  Building on recent advances in image generation, we present a data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising operations. We conduct experiments on four markup datasets: mathematical formulas (La), table layouts (HTML), sheet music (LilyPond), and molecular images (SMILES)
  arXiv  Detail & Related papers  (2022-10-11T04:56:12Z)
• 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)
• The Optimal Noise in Noise-Contrastive Learning Is Not What You Think [80.07065346699005]
  We show that deviating from this assumption can actually lead to better statistical estimators. In particular, the optimal noise distribution is different from the data's and even from a different family.
  arXiv  Detail & Related papers  (2022-03-02T13:59:20Z)
• Adaptive Multi-View ICA: Estimation of noise levels for optimal inference [65.94843987207445]
  Adaptive multiView ICA (AVICA) is a noisy ICA model where each view is a linear mixture of shared independent sources with additive noise on the sources. On synthetic data, AVICA yields better sources estimates than other group ICA methods thanks to its explicit MMSE estimator. On real magnetoencephalograpy (MEG) data, we provide evidence that the decomposition is less sensitive to sampling noise and that the noise variance estimates are biologically plausible.
  arXiv  Detail & Related papers  (2021-02-22T13:10:12Z)
• Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data [4.996878640124385]
  SINDy is a framework for the discovery of parsimonious dynamic models and equations from time-series data. We develop a variant of the SINDy algorithm that integrates automatic differentiation and recent time-stepping constrained by Rudy et al. We show the method can identify a diversity of probability distributions including Gaussian, uniform, Gamma, and Rayleigh.
  arXiv  Detail & Related papers  (2020-09-12T23:52:25Z)
• Learning while Respecting Privacy and Robustness to Distributional Uncertainties and Adversarial Data [66.78671826743884]
  The distributionally robust optimization framework is considered for training a parametric model. The objective is to endow the trained model with robustness against adversarially manipulated input data. Proposed algorithms offer robustness with little overhead.
  arXiv  Detail & Related papers  (2020-07-07T18:25:25Z)

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.