Better detectors and automated data collection have generated a flood of high-resolution cryo-EM maps, which in turn has renewed interest in improving methods for determining structure models corresponding to these maps. However, automatically fitting atoms to densities becomes difficult as their resolution increases and the refinement potential has a vast number of local minima. In practice, the problem becomes even more complex when one also wants to achieve a balance between a good fit of atom positions to the map, while also establishing good stereochemistry or allowing protein secondary structure to change during fitting. Here, we present a solution to this challenge using a maximum likelihood approach by formulating the problem as identifying the structure most likely to have produced the observed density map. This allows us to derive new types of smooth refinement potential-based on relative entropy-in combination with a novel adaptive force scaling algorithm to allow balancing of force-field and density-based potentials. In a low-noise scenario, as expected from modern cryo-EM data, the relative-entropy based refinement potential outperforms alternatives, and the adaptive force scaling appears to aid all existing refinement potentials. The method is available as a component in the GROMACS molecular simulation toolkit. Author summaryCryo-electron microscopy has gone through a revolution and now regularly produces data with 2 & ANGS; resolution. However, this data comes in the shape of density maps, and fitting atomic coordinates into these maps can be a labor-intensive and challenging problem. This is particularly valid when there are multiple conformations, flexible regions, or parts of the structure with lower resolution. In many cases it is also desirable to to understand how a molecule moves between such conformations. This can be addressed with molecular dynamics simulations using densities as target restraints, but the refinement potentials commonly used can distort protein structure or get stuck in local minima when the cryo-EM map has high resolution. This work derives new refinement potentials based on models of the cryo-EM scattering process that provide a gentle way to fit protein structures to densities in simulations, and we also suggest an automated heuristic way to balance the influence of the map and simulation force field.