The ages of star clusters and co-moving stellar groups contain essential information about the Milky Way. Their special properties and placement throughout the galactic disk make them excellent tracers of galactic structure and key components to unlocking its star formation history. Yet, even though the importance of stellar population ages has been widely recognized, their determination remains a challenging task often associated with highly model-dependent and uncertain results. We propose a new approach to this long-standing problem, which relies on empirical isochrones of known clusters extracted from high-quality observational data. These purely observation-based data products open up the possibility of relative age determination, free of stellar evolution model assumptions. For the derivation of the empirical isochrones, we used a combination of the statistical analysis tool principal component analysis for preprocessing and the supervised machine learning method support vector regression for curve extraction. To improve the statistical reliability of our result, we defined the empirical isochrone of a color-magnitude diagram (CMD) of a cluster as the median calculated from a set of $n_ boot =1000$ curves derived from bootstrapped data. The algorithm requires no physical priors, is computationally fast, and can easily be generalized over a large range of CMD combinations and evolutionary stages of clusters. We provide empirical isochrones in all Gaia DR2 and DR3 color combinations for 83 nearby clusters ($d < 500$ pc), which cover an estimated age range of 7 Myr to 3 Gyr. In doing so, we pave the way for a relative comparison between individual stellar populations based on an age-scaling ladder of empirical isochrones of known clusters. Furthermore, due to the exceptional precision of the available observational data, we report accurate lower main sequence empirical isochrones for many clusters in our sample, which are of special interest as this region is known to be especially complex to model. We validate our method and results by comparing the extracted empirical isochrones to cluster ages in the literature. We also investigate the added information that empirical isochrones covering the lower main sequence can provide on case studies of the IC 4665 cluster and the Meingast 1 stream. The archive of empirical isochrones offers a novel approach to validating age estimates and can be used as an age-scaling ladder or age brackets for new populations and serve as calibration data for further constraining stellar evolution models.
