Robot visuomotor policies are commonly formulated as autoregressive, diffusion-based, or more recently, flow matching models. Among them, Action-to-Action (A2A) flow matching improves inference efficiency by initializing generation from historical action priors rather than stochastic noise. However, stale historical motion patterns and entangled global visual representations can jointly reduce robustness under spatial out-of-distribution (OOD) shifts and visual distractors. In this work, we propose SlotFlow, an object-centric flow matching policy for robust visuomotor manipulation. SlotFlow decouples scene observations into semantic ("what") features and lightweight image-plane spatial ("where") cues to provide object-aware policy conditioning and current-state grounding. The semantic representation suppresses irrelevant background correlations, while the spatial cue improves adaptation to shifted object configurations. Extensive simulation and real-world experiments demonstrate improved robustness under visual distractors and severe spatial perturbations while preserving the low-step inference efficiency of A2A. Controlled initialization and perception ablations further identify object-centric grounding as a major source of the gains and show that it complements, rather than replaces, useful historical motion priors.

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