We introduce LiveSVG, a zero-shot approach for generating Scalable Vector Graphics (SVG) animations using video diffusion models. Current SVG animation methods struggle with complex motions: LLM-based code synthesis fails to express fine, non-rigid B\'ezier deformations, while Score Distillation Sampling (SDS) provides noisy gradients and often requires category-specific priors like skeletons. In contrast, LiveSVG fits vector geometry directly to an explicitly generated target video. Given an input SVG image and a motion prompt, we generate a previewable target video using a frozen image-to-video model, then fit the original SVG to this video via differentiable rendering. Our fitting stage is skeleton-free, utilizing a dual-level motion representation that combines per-group homographies for coarse articulation with per-path B\'ezier control-point offsets for local deformations. To resolve color-induced correspondence ambiguities during pixel-wise fitting, we introduce a novel sphere-packing recolorization strategy. We also present ChallengeSVG, a benchmark of complex, multi-object scenes that exposes the limitations of prior work. Evaluations demonstrate that LiveSVG significantly outperforms existing methods on both AniClipart and ChallengeSVG, establishing direct reference-video fitting as a practical, robust route to prompt-aligned and fully editable vector animation.