Impact statement: Manifold-learning flows have the potential to improve the efficiency with which scientists extract knowledge from large-scale experiments. Many phenomena have their most accurate description in terms of complex computer simulations which do not admit a tractable likelihood. In this common case, normalizing flows can be trained on synthetic data and used as a surrogate for the likelihood function, enabling high-quality inference on model parameters [21]. When the data have a manifold structure, manifold-learning flows may improve the quality and efficiency of this process further and ultimately contribute to scientific progress. We have demonstrated this with a real-world particle physics dataset, though the same technique is applicable to fields as diverse as neuroscience, systems biology, and epidemiology. All generative models carry a risk of being abused for the generation of fake data that are then masqueraded as real documents. This danger also applies to manifold-learning flows. While manifold-learning flows are currently far away from being able to generate realistic high-resolution images, videos, or audio, this concern should be kept in mind in the long term. Finally, the models we trained on image datasets of human faces clearly lack diversity. They reproduce and reinforce the biases inherent in the training data. Before using such (or other) models in any real-life application, it is crucial to understand, measure, and mitigate such biases.