Flow-LQR: Flow-Localized Linear Quadratic Regulator for Multi-Turn Image Editing

Instruction-based image editors enable iterative visual refinement, but successive edits can accumulate errors and degrade image quality. Our observations indicate that structured degradation arises even when an editor is asked to reconstruct an image without semantic changes, affecting both edited and unedited regions during subsequent editing. Preserving unedited pixels can limit this accumulation, but requires accurate localization, correction within edited regions, and coherent integration of generated and preserved content. We introduce Flow-LQR, a flow-localized linear quadratic regulator for stable multi-turn image editing. Complementary flow responses, calibrated by a reconstruction observation, identify the spatial region of the requested edit. We then reuse the flow predicted by the frozen diffusion transformer as an implicit representation of degradation. Latent residuals at the final denoising step provide disturbance observations in unchanged regions, and harmonic completion extends them into the edited region. A gain-preserving LQR coordinates generated and preserved content while compensating for this disturbance, followed by pixel restoration outside the localized region. We also introduce MTE-Bench for evaluating cumulative degradation over successive edits. Experiments demonstrate superior image preservation over open-source editors and the closed-source editor on both MTE-Bench and Banana100 benchmarks, with improved perceptual quality over the native backbone. Flow-LQR requires no backbone training or external segmentation models, and its disturbance observer reuses existing flow predictions without additional inference costs.