# DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations

arXiv: https://arxiv.org/abs/2204.08672 · HTML: https://mlsanity.com/paper/2204.08672/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 28 of its 71 references that are in the map.
- First posted on arXiv 19 Apr 2022.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming](https://mlsanity.com/paper/2105.07246/) (2021)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [Efficient Learning of Generative Models via Finite-Difference Score Matching](https://mlsanity.com/paper/2007.03317/) (2020)
- [Replica-exchange Nos'e-Hoover dynamics for Bayesian learning on large datasets](https://mlsanity.com/paper/1905.12569/) (2019)

## Built on by (most cited first, 24 of 24)

- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model](https://mlsanity.com/paper/2310.01678/) (2023)
- [Geometric Trajectory Diffusion Models](https://mlsanity.com/paper/2410.13027/) (2024)
- [A Hierarchical Training Paradigm for Antibody Structure-sequence Co-design](https://mlsanity.com/paper/2311.16126/) (2023)
- [Predicting mutational effects on protein-protein binding via a side-chain diffusion probabilistic model](https://mlsanity.com/paper/2310.19849/) (2023)
- [Structured Diffusion Models with Mixture of Gaussians as Prior Distribution](https://mlsanity.com/paper/2410.19149/) (2024)
- [Instructor-inspired Machine Learning for Robust Molecular Property Prediction](https://mlsanity.com/paper/2304.03906/) (2023)
- [A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics](https://mlsanity.com/paper/2401.15122/) (2024)
- [JAMUN: Bridging Smoothed Molecular Dynamics and Score-Based Learning for Conformational Ensembles](https://mlsanity.com/paper/2410.14621/) (2024)
- [Diffusion Twigs with Loop Guidance for Conditional Graph Generation](https://mlsanity.com/paper/2410.24012/) (2024)
- [Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Space](https://mlsanity.com/paper/2509.02196/) (2025)
- [TEMPO: Temporal Multi-scale Autoregressive Generation of Protein Conformational Ensembles](https://mlsanity.com/paper/2511.05510/) (2025)
- [Dynamics-inspired Structure Hallucination for Protein-protein Interaction Modeling](https://mlsanity.com/paper/2601.06214/) (2026)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Diff-PIC: Revolutionizing Particle-In-Cell Nuclear Fusion Simulation with Diffusion Models](https://mlsanity.com/paper/2408.02693/) (2024)
- [Atomic Trajectory Modeling with State Space Models for Biomolecular Dynamics](https://mlsanity.com/paper/2603.17633/) (2026)
- [Unbiasing Enhanced Sampling on a High-dimensional Free Energy Surface with Deep Generative Model](https://mlsanity.com/paper/2312.09404/) (2023)
- [Sifting through the Noise: A Survey of Diffusion Probabilistic Models and Their Applications to Biomolecules](https://mlsanity.com/paper/2406.01622/) (2024)
- [3D Interaction Geometric Pre-training for Molecular Relational Learning](https://mlsanity.com/paper/2412.02957/) (2024)
- [MDDM: A Molecular Dynamics Diffusion Model to Predict Particle Self-Assembly](https://mlsanity.com/paper/2501.17319/) (2025)
- [Potential Score Matching: Debiasing Molecular Structure Sampling with Potential Energy Guidance](https://mlsanity.com/paper/2503.14569/) (2025)
- [All-Atom GPCR-Ligand Dynamics Simulation via a Residual Latent Flow Mode](https://mlsanity.com/paper/2602.03902/) (2026)
- [Learning Implicit Bias in Generative Spaces for Accelerating Protein Dynamics Emulation](https://mlsanity.com/paper/2606.01833/) (2026)
- [SurfDesign: Effective Protein Design on Molecular Surfaces](https://mlsanity.com/paper/2606.07567/) (2026)

## Abstract (arXiv)

Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on intermediate variables such as the potential energy or force fields to update atomic positions, which requires additional computations to perform back-propagation. To waive this requirement, we propose a novel model called DiffMD by directly estimating the gradient of the log density of molecular conformations. DiffMD relies on a score-based denoising diffusion generative model that perturbs the molecular structure with a conditional noise depending on atomic accelerations and treats conformations at previous timeframes as the prior distribution for sampling. Another challenge of modeling such a conformation generation process is that a molecule is kinetic instead of static, which no prior works have strictly studied. To solve this challenge, we propose an equivariant geometric Transformer as the score function in the diffusion process to calculate corresponding gradients. It incorporates the directions and velocities of atomic motions via 3D spherical Fourier-Bessel representations. With multiple architectural improvements, we outperform state-of-the-art baselines on MD17 and isomers of C7O2H10 datasets. This work contributes to accelerating material and drug discovery.