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Auto-regressive (AR) models have recently made notable progress in image generation, achieving performance comparable to diffusion-based approaches. However, their computational intensity and sequential nature impede on-device deployment, causing disruptive latency. We address this via a cloud-device collaboration framework \textbf{CIAR}, which utilizes on-device self-verification to handle two key properties of visual synthesis: \textit{the vast token vocabulary} required for high-fidelity images and \textit{inherent spatial redundancy} which leads to extreme predictability in homogeneous regions, while object boundaries exhibit high uncertainty. Uniform verification wastes resources on such redundant tokens. Our solution centers on an on-device token uncertainty quantifier, which adopts continuous probability intervals to accelerate processing and make it feasible for large visual vocabularies instead of conventional discrete solution sets. Additionally, we incorporate a Interval-enhanced decoding module to further speed up decoding while maintaining visual fidelity and semantic consistency via a distribution alignment training strategy. Extensive experiments demonstrate that CIAR achieves a 2.18x speed-up and reduces cloud requests by 70\%, while preserving image quality compared to existing methods.