The ability to accurately align LLMs with diverse population groups on subjective questions would have great value. In this work, we show that adding simple supervision can more consistently improve the alignment of LLM-generated distributions with diverse population groups, as measured across three datasets spanning public health, public opinion, and values and beliefs. Beyond evaluating average alignment, we also report how alignment varies across specific groups. Our broad findings provide insights into the distributional alignment of LLM generations with diverse populations. By conducting evaluation over many LLMs and prompting strategies, we provide a benchmark to stimulate future research.