Formation-Consistent Flow Matching for Single-Image Defocus Deblurring

Single-image defocus deblurring seeks to recover an all-in-focus image from spatially varying defocus blur. Recent generative restoration methods based on Flow Matching can produce visually plausible results but may introduce hallucinated details that are not well supported by the observed blur. To address this limitation, we propose Formation-Consistent Flow Matching (FCFlow), a training framework that incorporates an effective defocus formation model into Flow Matching endpoint optimization. FCFlow learns an effective spatially varying circle-of-confusion (CoC) representation directly from the blurred input without requiring depth or CoC annotations. At a randomly sampled flow time, the predicted velocity is used to obtain a sharp endpoint proposal through single-step extrapolation. The proposal is decoded into image space and reblurred using the estimated CoC map, producing a formation discrepancy that is converted into a bounded latent endpoint correction. This correction refines endpoint optimization, thereby shaping the learned velocity field toward restorations that better explain the observed blur. The formation-aware endpoint optimization branch is omitted at inference, retaining standard Flow Matching sampling without additional formation-related overhead. Extensive experiments on DPDD, LFDOF, and RealDOF demonstrate state-of-the-art performance with 20-step inference, while strong single-step results further highlight the effectiveness of FCFlow in the low number of function evaluations (NFE) regime.