Retrieval-Augmented Initialization with Dual-Guided Inversion for Flow-Based Inverse Problem Solvers

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.

Flow-based generative models have emerged as powerful image priors for training-free inverse problem solving, capturing coherent semantics and fine-grained structure. Despite these strengths, existing flow-based inverse solvers primarily focus on the design of individual updates, largely overlooking spatio-temporal information allocation under a fixed number of function evaluations (NFEs). Temporally, insufficient early exploration can trap the flow trajectory in an incorrect semantic basin, whereas excessive allocation of NFEs to early stages leaves little budget for late-stage refinement. Spatially, data consistency provides direct constraints only within observed regions, whereas the recovery of missing regions relies mainly on the generative prior. To address these two issues, we introduce two complementary and training-free components, i.e., Spectrum-Adaptive Scheduling (SAS) and Measurement-Prioritized Attention (MPA). For temporal allocation, SAS distributes the available NFEs over flow time according to the degradation spectrum and logSNR geometry, thus better balancing semantic exploration and detail refinement. For spatial propagation, MPA exploits data-prior conflicts to guide information toward weakly constrained regions, thereby enhancing semantic and structural fidelity. Extensive experiments on standard image inverse problems, e.g., super-resolution, motion deblurring, and inpainting, demonstrate that the proposed components can be integrated into existing flow-based inverse solvers in a plug-and-play manner without retraining or additional flow-model evaluations, and can also significantly improve the restoration quality of existing solvers.

Existing generative model-based approaches to linear inverse problems typically use the acquired noisy measurement to condition or guide sampling in the image domain. In this work, we introduce Dual Flow, a novel joint flow model for solving linear inverse problems by jointly estimating the clean image and its corresponding noise-free measurement from the observation. Specifically, Dual Flow formulates image reconstruction and measurement denoising as a coupled estimation problem, using coupled flows in the image and measurement domains. The acquired noisy measurement $\mathbf{y}_0$ is used only to initialize the measurement state; thereafter, the image and measurement states are jointly updated based on their current values. By construction, the final image and measurement estimates are guaranteed to satisfy the underlying forward model. We derive the sampling updates for the joint flow and show that they are governed by the conditional mean of the clean image given the current joint state. We further derive a closed-form expression for a sufficient statistic of the joint state and show that the required conditional mean can be obtained by solving an image-domain Gaussian denoising problem involving operator-dependent, correlated noise. We train a velocity-prediction network using this formulation to estimate the conditional mean from the derived sufficient statistic. Dual Flow requires no hyperparameter tuning beyond selecting the number of inference steps and achieves substantially shorter reconstruction times than competing methods. Extensive experiments across various linear inverse problems and image datasets demonstrate state-of-the-art performance in both distortion metrics and perceptual quality. Additional analyses assess robustness to model mismatch, as well as the ability to generate diverse plausible reconstructions and characterize reconstruction uncertainty.