Large language models (LLMs) are increasingly used to simulate human populations and predict public opinion, yet there are concerns about their performance in cultural contexts outside the United States. Current practice relies on demographic agents, which are prompted with only basic demographic characteristics such as age, gender, and education. We introduce survey-anchored agents, a new approach that conditions LLMs on representative survey responses rather than demographics alone. Using the World Values Survey, which covers more than 50 societies worldwide, we compare the performance of survey-anchored agents against demographic agents across a wide range of political and cultural outcomes. Our results show that survey-anchored agents systematically achieve higher predictive accuracy, with the largest gains observed outside the United States where demographic cues are less informative. By grounding simulations in survey data, these agents capture cross-national variation in values and beliefs more effectively, narrowing the gap between model predictions and real-world human responses. This work provides a scalable framework for building culturally robust generative agents, and suggests that anchoring artificial populations in representative surveys can help ensure that LLM-based research and applications generalize across diverse social contexts.