aiqbench analysis
This research introduces P-Flow, a novel framework utilizing proxy gradients and Gaussian spherical projections to stabilize generative flow matching models for linear inverse problems. By circumventing the numerical instability associated with long-chain differentiation, it achieves robust performance in severe degradation scenarios while maintaining theoretical consistency through Bayesian analysis. The work advances machine learning methodologies specifically tailored for high-dimensional restoration tasks under extreme noise conditions.
P-Flow: Proxy-gradient Flows for Linear Inverse Problems
arXiv:2605.08328v3 Announce Type: replace Abstract: Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate differentiating through unrolled paths, leading to numerical instability and prohibitive computational overhead. To address this, we propose P-Flow, a framework that stabilizes the reconstruction process by leveraging a proxy gradient to update the source point. This approach effectively circumvents the numerical instability and memory overhead of long-chain differentiation. To ensure consistency with the prior distribution, we employ a Gaussian spherical projection motivated by the concentration of measure phenomenon in high-dimensional spaces. We further provide a theoretical analysis for P-Flow based on Bayesian theory and Lipschitz continuity. Experiments across diverse restoration tasks demonstrate that P-Flow delivers competitive performance, especially under extreme degradations such as severely ill-posed conditions and high measurement noise.
Abstract:Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate differentiating through unrolled paths, leading to numerical instability and prohibitive computational overhead. To address this, we propose P-Flow, a framework that stabilizes the reconstruction process by leveraging a proxy gradient to update the source point. This approach effectively circumvents the numerical instability and memory overhead of long-chain differentiation. To ensure consistency with the prior distribution, we employ a Gaussian spherical projection motivated by the concentration of measure phenomenon in high-dimensional spaces. We further provide a theoretical analysis for P-Flow based on Bayesian theory and Lipschitz continuity. Experiments across diverse restoration tasks demonstrate that P-Flow delivers competitive performance, especially under extreme degradations such as severely ill-posed conditions and high measurement noise.
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)
arXiv:2605.08328 [cs.LG]
(or arXiv:2605.08328v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.08328 Focus to learn more arXiv-issued DOI via DataCite
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