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$360^\circ$ videos offer a hyper-immersive experience that allows the viewers to explore a dynamic scene from full 360 degrees. To achieve more accessible and personalized content creation in $360^\circ$ video format, we seek to lift standard perspective videos into $360^\circ$ equirectangular videos. To this end, we introduce **Imagine360**, the first perspective-to-$360^\circ$ video generation framework that creates high-quality $360^\circ$ videos with rich and diverse motion patterns from video anchors. Imagine360 learns fine-grained spherical visual and motion patterns from limited $360^\circ$ video data with several key designs. **1)** Firstly we adopt the dual-branch design, including a perspective and a panorama video denoising branch to provide local and global constraints for $360^\circ$ video generation, with motion module and spatial LoRA layers fine-tuned on $360^\circ$ videos. **2)** Additionally, an antipodal mask is devised to capture long-range motion dependencies, enhancing the reversed camera motion between antipodal pixels across hemispheres. **3)** To handle diverse perspective video inputs, we propose rotation-aware designs that adapt to varying video masking due to changing camera poses across frames. **4)** Lastly, we introduce a new 360 video dataset featuring 10K high-quality, trimmed 360 video clips with structured motion to facilitate training. Extensive experiments show Imagine360 achieves superior graphics quality and motion coherence with our curated dataset among state-of-the-art $360^\circ$ video generation methods. We believe Imagine360 holds promise for advancing personalized, immersive $360^\circ$ video creation.