# Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Space

arXiv: https://arxiv.org/abs/2509.02196 · HTML: https://mlsanity.com/paper/2509.02196/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 75 references that are in the map.
- First posted on arXiv 2 Sep 2025.

## Builds on (most cited first, 30 of 42)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Generative Modeling of Molecular Dynamics Trajectories](https://mlsanity.com/paper/2409.17808/) (2024)
- [Transferable Boltzmann Generators](https://mlsanity.com/paper/2406.14426/) (2024)
- [Equivariant Graph Neural Operator for Modeling 3D Dynamics](https://mlsanity.com/paper/2401.11037/) (2024)
- [Flow-matching -- efficient coarse-graining of molecular dynamics without forces](https://mlsanity.com/paper/2203.11167/) (2022)
- [DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations](https://mlsanity.com/paper/2204.08672/) (2022)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [Variational Encoding of Complex Dynamics](https://mlsanity.com/paper/1711.08576/) (2017)
- [Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional](https://mlsanity.com/paper/2504.18506/) (2025)
- [Deep Generative Markov State Models](https://mlsanity.com/paper/1805.07601/) (2018)

## Built on by (most cited first, 3 of 3)

- [World Models as Group Actions](https://mlsanity.com/paper/2605.24578/) (2026)
- [Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamics](https://mlsanity.com/paper/2604.25244/) (2026)
- [All-Atom GPCR-Ligand Dynamics Simulation via a Residual Latent Flow Mode](https://mlsanity.com/paper/2602.03902/) (2026)

## Abstract (arXiv)

Simulating the long-timescale dynamics of biomolecules is a central challenge in computational science. While enhanced sampling methods can accelerate these simulations, they rely on pre-defined collective variables that are often difficult to identify, restricting their ability to model complex switching mechanisms between metastable states. A recent generative model, LD-FPG, demonstrated that this problem could be bypassed by learning to sample the static equilibrium ensemble as all-atom deformations from a reference structure, establishing a powerful method for all-atom ensemble generation. However, while this approach successfully captures a system's probable conformations, it does not model the temporal evolution between them. We introduce the Graph Latent Dynamics Propagator (GLDP), a modular component for simulating dynamics within the learned latent space of LD-FPG. We then compare three classes of propagators: (i) score-guided Langevin dynamics, (ii) Koopman-based linear operators, and (iii) autoregressive neural networks. Within a unified encoder-propagator-decoder framework, we evaluate long-horizon stability, backbone and side-chain ensemble fidelity, and temporal kinetics via TICA. Benchmarks on systems ranging from small peptides to mixed-topology proteins and large GPCRs reveal that autoregressive neural networks deliver the most robust long rollouts and coherent physical timescales; score-guided Langevin best recovers side-chain thermodynamics when the score is well learned; and Koopman provides an interpretable, lightweight baseline that tends to damp fluctuations. These results clarify the trade-offs among propagators and offer practical guidance for latent-space simulators of all-atom protein dynamics.