This paper addresses a major computational challenge: long-time dynamics simulations of biomolecules. While advanced sampling techniques can accelerate simulations, they often rely on predefined sets of variables that are difficult to identify. A recent generative model, LD-FPG, has demonstrated a way to circumvent this problem by learning to sample statically equilibrium ensembles of all atomic variants from a reference structure, establishing a robust method for generating all-atom ensembles. However, while this approach successfully captures the system's likely conformations, it does not model the temporal evolution between conformations. This study adds a temporal propagator operating within the learned latent space to LD-FPG and compares three methods: (i) score-based Langevin dynamics, (ii) Koopman-based linear operators, and (iii) autoregressive neural networks. Within a unified encoder-propagator-decoder framework, we evaluate long-term stability, backbone and side-chain ensemble fidelity, and the functional free energy landscape. Autoregressive neural networks provide the most robust long-term rollout, score-based Langevin best reconstructs side-chain thermodynamics when the scores are well-trained, and Koopman provides an interpretable and lightweight baseline that tends to damp fluctuations. These results clarify the tradeoffs between propagators and provide practical guidance for latent-space simulators of all-atom protein dynamics.
