Diffusion models have shown impressive results in text-to-image synthesis. Using massive datasets of captioned images, diffusion models learn to generate raster images of highly diverse objects and scenes. However, designers frequently use vector representations of images like Scalable Vector Graphics (SVGs) for digital icons, graphics and stickers. Vector graphics can be scaled to any size, and are compact. In this work, we show that a text-conditioned diffusion model trained on pixel representations of images can be used to generate SVG-exportable vector graphics. We do so without access to large datasets of captioned SVGs. Instead, inspired by recent work on text-to-3D synthesis, we vectorize a text-to-image diffusion sample and fine-tune with a Score Distillation Sampling loss. By optimizing a differentiable vector graphics rasterizer, our method distills abstract semantic knowledge out of a pretrained diffusion model. By constraining the vector representation, we can also generate coherent pixel art and sketches. Our approach, VectorFusion, produces more coherent graphics than prior works that optimize CLIP, a contrastive image-text model.