analiza aiqbench
This paper introduces $\beta$-Flow, a unified framework for solving linear inverse problems by generalizing flow-matching and diffusion models through exact Gaussian conditioning. By decoupling trajectory priors from network gradients via a Kalman update, the method offers flexible prior control that adapts to data sparsity without requiring bespoke implementations for each model class. The approach achieves state-of-the-art performance across seven inverse problems, demonstrating how theoretical unification can improve practical sampling efficiency in generative modeling.
Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning
arXiv:2610.13812v1 Announce Type: new Abstract: Flow-matching and diffusion models are increasingly used as priors for linear inverse problems, however, most methods are bespoke to one class of trajectory prior. Plug-and-play methods have been proposed, however these implicitly decorrelate the guided trajectory, resulting in broad priors that can struggle when data is sparse. This work proposes $\beta$-Flow: a general plug-and-play method indexed by a correlation parameter $\beta$ that generalises over flow, diffusion, and decorrelated priors, and a confidence parameter $\kappa$ that controls how strongly the path distribution is enforced. Each step requires only one forward evaluation of a denoising network, followed by a Gaussian conditioning step. This step is an exact Kalman update that is not dependent on network gradients. We show that many existing guided samplers can be interpreted as instances or approximations of our method, each implicitly using a different trajectory prior and operator in place of the Kalman gain. From this viewpoint, we provide a qualitative comparison of methods in terms of their implicit biases and assumptions. We demonstrate consistently state-of-the-art level performance across 7 inverse problems over 4 datasets in terms of PSNR and SSIM. Moreover, we demonstrate the utility of this prior control, by showing that confident high correlations (strict priors) work best when observations are less informative, while low correlation is preferred when observations are more informative, reflecting the complementary roles of the prior and likelihood in Bayesian inference.
Abstract:Flow-matching and diffusion models are increasingly used as priors for linear inverse problems, however, most methods are bespoke to one class of trajectory prior. Plug-and-play methods have been proposed, however these implicitly decorrelate the guided trajectory, resulting in broad priors that can struggle when data is sparse. This work proposes $\beta$-Flow: a general plug-and-play method indexed by a correlation parameter $\beta$ that generalises over flow, diffusion, and decorrelated priors, and a confidence parameter $\kappa$ that controls how strongly the path distribution is enforced. Each step requires only one forward evaluation of a denoising network, followed by a Gaussian conditioning step. This step is an exact Kalman update that is not dependent on network gradients. We show that many existing guided samplers can be interpreted as instances or approximations of our method, each implicitly using a different trajectory prior and operator in place of the Kalman gain. From this viewpoint, we provide a qualitative comparison of methods in terms of their implicit biases and assumptions. We demonstrate consistently state-of-the-art level performance across 7 inverse problems over 4 datasets in terms of PSNR and SSIM. Moreover, we demonstrate the utility of this prior control, by showing that confident high correlations (strict priors) work best when observations are less informative, while low correlation is preferred when observations are more informative, reflecting the complementary roles of the prior and likelihood in Bayesian inference.
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)
arXiv:2610.13812 [cs.LG]
(or arXiv:2610.13812v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.13812 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 329 cuvinte
Subiecte conexe
Exact Posterior Score Estimation for Solving Linear Inverse Problems
arXiv · 16 iun. 2026
Interacting particle guidance for sampling reward-tilted generative priors
arXiv · 30 sept. 2026
AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation
arXiv · 30 sept. 2026
Scalable Diffusion SBI for Compositional Inference under Simulator Misspecification
arXiv · 30 sept. 2026