Neural processes (NPs) are models for meta-learning which output uncertainty estimates. So far, most studies of NPs have focused on low-dimensional datasets of highly-correlated tasks. While these homogeneous datasets are useful for benchmarking, they may not be representative of realistic transfer learning. In particular, applications in scientific research may prove especially challenging due to the potential novelty of meta-testing tasks. Molecular property prediction is one such research area that is characterized by sparse datasets of many functions on a shared molecular space. In this paper, we study the application of graph NPs to molecular property prediction with DOCKSTRING, a diverse dataset of docking scores. Graph NPs show competitive performance in few-shot learning tasks relative to supervised learning baselines common in chemoinformatics, as well as alternative techniques for transfer learning and meta-learning. In order to increase meta-generalization to divergent test functions, we propose fine-tuning strategies that adapt the parameters of NPs. We find that adaptation can substantially increase NPs' regression performance while maintaining good calibration of uncertainty estimates. Finally, we present a Bayesian optimization experiment which showcases the potential advantages of NPs over Gaussian processes in iterative screening. Overall, our results suggest that NPs on molecular graphs hold great potential for molecular property prediction in the low-data setting.Scientific contributionNeural processes are a family of meta-learning algorithms which deal with data scarcity by transferring information across tasks and making probabilistic predictions. We evaluate their performance on regression and optimization molecular tasks using docking scores, finding them to outperform classical single-task and transfer-learning models. We examine the issue of generalization to divergent test tasks, which is a general concern of meta-learning algorithms in science, and propose strategies to alleviate it.