FIG: Flow with Interpolant Guidance for Linear Inverse Problems
Yici Yan Yichi Zhang Xiangming Meng Zhizhen Zhao
Diffusion and flow matching models have recently been used to solve various linear inverse problems in image restoration, such as super-resolution and inpainting. Using a pre-trained diffusion or flow-matching model as a prior, most existing methods modify the reverse-time sampling process by incorporating the likelihood information from the measurement. However, they struggle in challenging scenarios, such as high measurement noise or severe ill-posedness. In this paper, we propose Flow with Interpolant Guidance (FIG), an algorithm where reverse-time sampling is efficiently guided with measurement interpolants through theoretically justified schemes. Experimentally, we demonstrate that FIG efficiently produces highly competitive results on a variety of linear image reconstruction tasks on natural image datasets, especially for challenging tasks. Our code is available at: https://riccizz.github.io/FIG/.
Flow Matching, Diffusion Model, Linear Inverse Problems
We propose Flow with Interpolant Guidance (FIG), where the reverse-time sampling is efficiently guided with measurement interpolants to solve linear inverse problems.