Converting a raster image into a resolution-independent, stroke-editable vector sketch while faithfully preserving both structural contours and tonal texture remains challenging: raster-space rendering pipelines are difficult to edit at the stroke level, while generation-from-scratch vectorization methods struggle to remain faithful to an arbitrary input image. We present SketchForge, a training-free framework that converts an input raster image into a resolution-independent SVG sketch through per-instance test-time optimization of Bezier curves, requiring no additional training or fine-tuning. Strokes are seeded via a contour and attention-guided initialization, then refined by a vector-native differentiable rendering pipeline that decouples structural contour strokes from free-form texture strokes under dedicated objectives, composited via multiply-blend layering. Extensive experiments show that SketchForge consistently outperforms existing vector-based baselines in structural fidelity and generation quality. Project page: https://khangcntn123.github.io/SketchForge

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