Diffusion-based video super-resolution (VSR) methods deliver strong perceptual quality but are often unsuitable for latency-sensitive scenarios due to reliance on future frames and expensive multi-step denoising. We propose Stream-DiffVSR, a causally conditioned diffusion framework for efficient online VSR. Operating strictly on past frames, Stream-DiffVSR integrates a four-step distilled denoiser for fast inference, an Auto-regressive Temporal Guidance (ARTG) module that injects motion-aligned cues during latent denoising, and a lightweight temporal-aware decoder with a Temporal Processor Module (TPM) to enhance detail and temporal coherence. Unlike chunk-wise streaming inference, our strictly frame-by-frame causal design avoids sequence-level waiting, substantially reducing time-to-first-frame and end-to-end latency. Stream-DiffVSR processes 720p frames in 0.328 seconds on an RTX 4090 and consistently outperforms prior diffusion-based baselines. Compared with the online state-of-the-art TMP, it improves perceptual quality (LPIPS +0.095) while reducing latency by over 130x. Moreover, Stream-DiffVSR substantially lowers time-to-first-frame for diffusion-based VSR, reducing initial delay from over 4600 seconds to 0.328 seconds, making diffusion-based VSR markedly more practical for low-latency online and streaming deployment. Project page: https://jamichss.github.io/stream-diffvsr-project-page/