Molecular dynamics simulations of proteins are limited by short integration time steps to millisecond time scales. We developed latent space simulators (LSS) based on three back-to-back deep learning networks designed to (i) learn the slow collective motions of the system, (ii) efficiently propagate the system dynamics in this slow latent space, and (iii) generatively decode from the latent space back up to the all-atom configurations. In an application to Trp-cage mini-protein trained over modest molecular simulation data we produced ultra-long synthetic trajectories at one-million-fold lower cost than molecular dynamics simulation to achieve orders of magnitude lower uncertainties in thermodynamic averages and kinetic rates. The improved understanding of protein structure and function and its interplay with evolutionary mutations underpin our deep representational discovery and exploitation of the collective latent evolutionary modes in natural proteins.