The challenge of automatically synthesizing high-quality vector fonts, particularly for writing systems (e.g., Chinese) consisting of huge amounts of complex glyphs, remains unsolved. Existing font synthesis techniques fall into two categories: 1) methods that directly generate vector glyphs, and 2) methods that initially synthesize glyph images and then vectorize them. However, the first category often fails to construct complete and correct shapes for complex glyphs, while the latter struggles to efficiently synthesize high-resolution (i.e., 1024 $\times$ 1024 or higher) glyph images while preserving local details. In this paper, we introduce HFH-Font, a few-shot font synthesis method capable of efficiently generating high-resolution glyph images that can be converted into high-quality vector glyphs. More specifically, our method employs a diffusion model-based generative framework with component-aware conditioning to learn different levels of style information adaptable to varying input reference sizes. We also design a distillation module based on Score Distillation Sampling for 1-step fast inference, and a style-guided super-resolution module to refine and upscale low-resolution synthesis results. Extensive experiments, including a user study with professional font designers, have been conducted to demonstrate that our method significantly outperforms existing font synthesis approaches. Experimental results show that our method produces high-fidelity, high-resolution raster images which can be vectorized into high-quality vector fonts. Using our method, for the first time, large-scale Chinese vector fonts of a quality comparable to those manually created by professional font designers can be automatically generated.