We introduce Instruct-SkillMix, an automated approach for creating diverse, high quality SFT data for instruction-following. The pipeline involves two stages, each leveraging an existing powerful LLM: (1) Skill extraction: uses the LLM to extract core skills'' for instruction-following, either by directly prompting the model, or prompting it to identify skills needed for existing datasets (Didolkar et al., 2024); (2) Data generation: uses the powerful LLM to generate (instruction, response) data that exhibit a randomly chosen pair of these skills. Here, the use of random skill combinations promotes diversity and difficulty.Vanilla SFT (i.e., no PPO, DPO, or RL methods) on data generated from Instruct-SkillMix leads to strong gains on instruction following benchmarks such as AlpacaEval 2.0, MT-Bench, and WildBench. With just 4K examples, LLaMA-3-8B-Base achieves 42.76% length-controlled win rate on AlpacaEval 2.0, a level similar to frontier models like Claude 3 Opus and LLaMA-3.1-405B-Instruct. The estimated cost of creating the dataset is $600.Ablation studies also suggest plausible reasons for why creating open instruction-tuning datasets via naive crowd-sourcing has proved difficult. In our dataset, adding 20% low quality answers (shirkers'') causes performance to plummet, sometimes catastrophically.The Instruct-SkillMix pipeline is flexible and the ideas are adaptable to other settings.