<p>Existing video super-resolution (VSR) methods are typically restricted to fixed integer scales, limiting their flexibility in real-world applications. While applying arbitrary-scale image super-resolution (ASISR) to each frame enables scale adaptation, it neglects temporal modeling; conversely, post-interpolation after fixed-scale VSR retains temporal consistency but introduces blurring and distortions. To address these limitations, we propose SAVSR, a unified end-to-end framework for arbitrary-scale video super-resolution that jointly models scale variation and spatiotemporal consistency. To capture long-term dependencies and mitigate structural drift across frames, we introduce an iterative bidirectional alignment (IBA) architecture that leverages both recurrent and iterative designs. We further propose the omni-dimensional scale-attention convolution (OSConv) and a spatiotemporal-aware upsampling (STAU) module to enable dynamic scale adaptivity and temporally-aware reconstruction within a single model. SAVSR achieves state-of-the-art performance across arbitrary, asymmetric, and out-of-distribution scales. Building on SAVSR, we further propose a recurrent locally omniscient framework and extend SAVSR to SAVSR++, a lightweight, more stable, and generalizable architecture for arbitrary-scale VSR. Extensive experiments demonstrate that SAVSR++ achieves improved robustness and generalization on complex, long-sequence videos.</p>