arXiv Machine Learning By Alexander Denker, Zeljko Kereta, Carola-Bibiane Sch\"onlieb, Moshe Eliasof

Trajectory Stitching for Solving Inverse Problems with Flow-Based Models

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The paper introduces MS-Flow, a method that represents a flow-based generative model’s trajectory as a sequence of intermediate latent states instead of a single initial code. By enforcing local flow dynamics and coupling trajectory segments with matching penalties, the approach alternates between updating latent states and ensuring consistency with observed data. This strategy reduces memory usage and improves reconstruction quality on tasks such as image inpainting, super‑resolution, and computed tomography.

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arXiv Machine Learning
Aug 3

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.

By Zehua Jiang, Fenghao Zhu, Xinquan Wang, Chongwen Huang, Zhaoyang Zhang
arXiv Computer Vision
Sep 18

FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants

FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling (SGS) with Langevin dynamics for the likelihood step and Stochastic Interpolants (SI) for the prior step. By integrating a pretrained flow model into the prior step via SI's reverse-time SDE and a novel timestep correction, FlowSGS reduces the number of network evaluations compared to plug‑and‑play diffusion samplers. Experiments demonstrate state‑of‑the‑art performance on various inverse problems, including the first flow‑based solution to a nonlinear inverse problem (Fourier phase retrieval).

By Tianao Li, Xinhui Qian, Emma Alexander