Trajectory Stitching for Solving Inverse Problems with Flow-Based Models
This addresses computational bottlenecks for researchers and practitioners using flow-based models in inverse problems, representing an incremental improvement over existing optimization methods.
The paper tackles the high memory costs and numerical instability in solving inverse problems with flow-based models by proposing MS-Flow, which uses intermediate latent states and trajectory-matching penalties, resulting in reduced memory consumption and improved reconstruction quality on tasks like inpainting and super-resolution.
Flow-based generative models have emerged as powerful priors for solving inverse problems. One option is to directly optimize the initial latent code (noise), such that the flow output solves the inverse problem. However, this requires backpropagating through the entire generative trajectory, incurring high memory costs and numerical instability. We propose MS-Flow, which represents the trajectory as a sequence of intermediate latent states rather than a single initial code. By enforcing the flow dynamics locally and coupling segments through trajectory-matching penalties, MS-Flow alternates between updating intermediate latent states and enforcing consistency with observed data. This reduces memory consumption while improving reconstruction quality. We demonstrate the effectiveness of MS-Flow over existing methods on image recovery and inverse problems, including inpainting, super-resolution, and computed tomography.