In contrast to the experimental process, which generates an average structure, molecular dynamics (MD) simulations enable the simulation of molecular behavior at an atomic level and high temporal resolution across diverse thermodynamic conditions. However, MD simulations have been and will continue to be fundamentally limited by slow sampling and hardware constraints since the Newtonian equations should be solved for motions of every atom in a system. Conversely, machine learning techniques, particularly deep learning-based MD models, have been utilized in the MD field, whether in force field development, simulation analysis, or sampling. Diffusion models are considered a distinct class of deep generative models due to their capabilities in generating precise details. This method has been applied in various fields such as image editing and computer vision. This study introduced a novel application of the diffusion model in the generation of synthetic trajectories in a low-dimensional space that can be used in the calculation of the free-energy surface. First, a simplified two-dimensional model followed by an overdamped Langevin dynamics equation is used as a training data set. The data set showed deviations from the analytical form of the Muller potential surface, but the diffusion model revealed improved accuracy to the ground truth. Following this stage, this model was applied to a small peptide (alanine dipeptide) as well as a membrane transporter to assess its accuracy in generating free energy. This novel method is able to accelerate significantly the MD synthetic trajectories while accurately reconstructing the free-energy surface.
Jamali et al. (Sun,) studied this question.