  We present a flow-based generative approach to emulate grids of stellar
evolutionary models. By interpreting the input parameters and output properties
of these models as multi-dimensional probability distributions, we train
conditional normalizing flows to learn and predict the complex relationships
between grid inputs and outputs in the form of conditional joint distributions.
Leveraging the expressive power and versatility of these flows, we showcase
their ability to emulate a variety of evolutionary tracks and isochrones across
a continuous range of input parameters. In addition, we describe a simple
Bayesian approach for estimating stellar parameters using these flows and
demonstrate its application to asteroseismic datasets of red giants observed by
the Kepler mission. By applying this approach to red giants in open clusters
NGC 6791 and NGC 6819, we illustrate how large age uncertainties can arise when
fitting only to global asteroseismic and spectroscopic parameters without prior
information on initial helium abundances and mixing length parameter values. We
also conduct inference using the flow at a large scale by determining revised
estimates of masses and radii for 15,388 field red giants. These estimates show
improved agreement with results from existing grid-based modelling, reveal
distinct population-level features in the red clump, and suggest that the
masses of Kepler red giants previously determined using the corrected
asteroseismic scaling relations have been overestimated by 5-10%.
