A primary goal in computational biophysics is to harness experimental measurements to obtain information on the structure and dynamics of biomolecules. However, most biophysical techniques such as NMR and EPR spectroscopy provide signals that arise from an ensemble of multiple molecular conformations. Thus, it is typically not straightforward to extract detailed structural information from the experimental data. A possible strategy is to bias the conformational sampling obtained in a molecular dynamics simulations in reference to the experimental data, under the so-called maximum entropy principle. Recent practical formulations of this approach involve simulations carried out over multiple replicas or iterative ensemble-correction procedures based on the determination of several (Lagrange) parameters. Here, we present an alternative, self-learning approach to sample molecular ensembles compatible with experimental data with the minimal possible bias on the simulation trajectories. The method does not require multiple replicas and is based on adding an adaptive bias potential during the simulation that discourages the sampling of conformations that are not consistent with the experimental measurements. To illustrate this approach, we applied this novel simulation technique to spin-labeled T4-lysozyme, targeting a set of spin-spin distance distributions measured by DEER/EPR spectroscopy. We show how the proposed method is able to efficiently sample the experimental distance distributions without altering uncorrelated degrees of freedom. We anticipate that this new simulation approach will be widely useful to obtain conformational ensembles compatible with diverse types of experimental measurements of biomolecular dynamics.