Organizations: School of Computer Science, Peking University · BioGeometry · Mila - Québec AI Institute · Université de Montréal · HEC Montréal · CIFAR AI Chair
Understanding the dynamic behavior of biomolecules is fundamental to elucidating biological function and facilitating drug discovery. While Molecular Dynamics (MD) simulations provide a rigorous physical basis for studying these dynamics, they remain computationally expensive for long timescales. Conversely, recent deep generative models accelerate conformation generation but are typically either failing to model temporal relationship or built only for monomeric proteins. To bridge this gap, we introduce ATMOS, a novel generative framework based on State Space Models (SSM) designed to generate atom-level MD trajectories for biomolecular systems. ATMOS integrates a Pairformer-based state transition mechanism to capture long-range temporal dependencies, with a diffusion-based module to decode trajectory frames in an autoregressive manner. ATMOS is trained across crystal structures from PDB and conformation trajectory from large-scale MD simulation datasets including mdCATH and MISATO. We demonstrate that ATMOS achieves state-of-the-art performance in generating conformation trajectories for both protein monomers and complex protein-ligand systems. By enabling efficient inference of atomic trajectory of motions, this work establishes a promising foundation for modeling biomolecular dynamics.
Figures & tables
Figure 1: Overview of the Proposed Atomic Trajectory Modeling Framework.
Conformation Models
Trajectory Models
Reference MD traj.
AlphaFlow-MD
ESMFlow-MD
MDGen
TEMPO
ConfRover
ATMOS
Predicting flexibility
Pairwise RMSD r↑
0.61
0.46
0.65
0.73
0.69
0.92
0.96
Global RMSF r↑
0.57
0.47
0.67
0.61
0.62
0.90
0.95
Per-target RMSF r↑
0.85
0.80
0.77
0.52
0.81
0.89
0.95
Distributional accuracy
Root mean W2 -dist. ↓
3.40
5.00
3.86
4.98
4.52
2.70
1.89
MD PCA W2 -dist. ↓
2.26
2.16
2.75
2.38
3.04
1.79
1.67
Table 1: Evaluation on mdCATH . The best scores are highlighted in bold and the second-best scores are underlined . r : Pearson correlation; J : Jaccard similarity; W2 : 2-Wasserstein distance.
Figure 2: Case Study on 1s79a00 , a target from the test set of mdCATH. (A) the visualization of ensemble from MD simulation (reference) or ATMOS (sampled). (B) The visualization of snapshot at specific frame index. (C) The RMSF versus the residue index. (D) The moving RMSD to the initial structure (frame 0) along the trajectory frames.
Model
Inference Time (Hour)
Peak Mem (GB)
MD Simulation
> 10
< 1
ConfRover
0.467
22.53
ATMOS
0.174
3.445
ATMOS-Parallel
0.044
6.117
Table 2: Efficiency evaluation on the 1gnla01 protein (139 AA). MD simulation is performed with Amber24 on GPU ( Salomon-Ferrer et al., 2013 ) , employing an integration time step of 4 fs.
Method
per-target RMSF r↑
Root mean W2 -dist ↓
Steric Clashes ↓
t-RMSD Error ↓
Ligand
DenoisingLD ( Wu and Li, 2023 )
0.028
0.791
1.825
34.01
GNNMD ( Siebenmorgen et al., 2024 )
0.135
0.870
81.69
0.672
NeuralMD-SDE ( Liu et al., 2025 )
0.574
0.698
7.667
0.698
VerletMD ( Liu et al., 2025 )
0.456
36.83
14.67
43.78
DynamicBind ( Lu et al., 2024b )
0.678
1.470
7.113
-
Boltz-2 ( Passaro et al., 2025 )
0.613
1.237
0.210
-
Table 3: Evaluation on MISATO . The best scores are highlighted in bold and the second-best scores are underlined . r : Pearson correlation; W2 : 2-Wasserstein distance. Boltz‑2 is trained on the entire MISATO dataset, which may lead to data leakage; we include it as a strong but potentially optimistic baseline.
Metric
ATMOS
w/o bi-level sampling
ODE
Pairwise RMSD r↑
0.92
0.88
0.73
Global RMSF r↑
0.90
0.84
0.64
Per-target RMSF r↑
0.89
0.85
0.63
Root mean W2 -dist. ↓
2.70
3.06
3.89
MD PCA W2 -dist. ↓
1.79
2.09
2.73
Joint PCA W2 -dist. ↓
2.32
2.61
3.28
Table 4: Ablation study on sampling protocol .
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 3: Detailed architecture of our framework. BIF: Bidirectional Information Flow.
Hyperparameter
Value
Number of Pairformer blocks
4
Single representation dimension
384
Pair representation dimension
128
Triangle multiplication hidden dimension
128
Number of triangle attention heads
4
Transition layer expanding factor
4
Appendix
Table 5: Architectural hyperparameters for the modified Pairformer.
Generating molecular dynamics (MD) trajectories using deep generative models has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-dimensional MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pretraining for MD trajectory generation. Specifically, we first train a diffusion-based structure generation model on a large-scale conformer dataset, on top of which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simulation, and interpolation tasks, and further extend our framework and analysis to tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.
Molecular dynamics (MD) simulations are a principled but computationally expensive approach for studying protein conformational variability, making it challenging to generate large ensembles of structures or characterize transitions between metastable conformations. AI methods for upsampling MD simulations have been developed recently but struggle due to difficulties of sampling complex, high-dimensional molecular distributions. One avenue these methods overlook is to learn a latent space where such sampling becomes easier. To address this, we introduce ProtScape, a generative geometric deep learning framework that learns structure and energy-aware representations of protein conformational landscapes from MD simulations. ProtScape represents protein conformations using an equivariant graph neural network and a multiscale deep wavelet transform that captures local geometric interactions and nonlocal collective motions. This latent representation is dual-organized: 1) by structure captured by wavelet transform layers, via reconstruction error; 2) by energy using a Laplacian energy smoothness penalty. This structured latent space enables meaningful generation and exploration of protein conformations. ProtScape supports multiple generative modes: 1) ensemble generation, which upsamples ensembles given limited MD trajectories flow matching from noise to the organized manifold of conformations, 2) minimum-energy path generation between two high-energy conformations, guided by energy using a nudged elastic band, and 3) energy-descent, which generates trajectories toward lower energies from a high-energy conformation using gradient descent, thereby hypothesizing folding or other stabilizing trajectories. Organizing a latent space by structure and energy lets one representation support ensemble sampling, minimum-energy path finding and energy-guided descent on the same conformational landscape.
Siddharth Viswanath, Xingzhi Sun, Lucas Lee +9
Department of Computer Science, Yale University · Department of Genetics, Yale University · Program in Computing, Boise State University +2
Recent 3D molecular generation methods primarily use asynchronous auto-regressive or synchronous diffusion models. While auto-regressive models build molecules sequentially, they're limited by a short horizon and a discrepancy between training and inference. Conversely, synchronous diffusion models denoise all atoms at once, offering a molecule-level horizon but failing to capture the causal relationships inherent in hierarchical molecular structures. We introduce Equivariant Asynchronous Diffusion (EAD) to overcome these limitations. EAD is a novel diffusion model that combines the strengths of both approaches: it uses an asynchronous denoising schedule to better capture molecular hierarchy while maintaining a molecule-level horizon. Since these relationships are often complex, we propose a dynamic scheduling mechanism to adaptively determine the denoising timestep. Experimental results show that EAD achieves state-of-the-art performance in 3D molecular generation.
Junyi An, Chao Qu, Yun-Fei Shi +3
Shanghai Academy of Artificial Intelligence for Science, SAIS · Artificial Intelligence Innovation and Incubation (AI3) Institute, Fudan University