# Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model

arXiv: https://arxiv.org/abs/2310.01678 · HTML: https://mlsanity.com/paper/2310.01678/

## Key facts

- Cited by 16 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 23 of its 74 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## 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, 23 of 23)

- [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)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems](https://mlsanity.com/paper/2307.08423/) (2023)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learning](https://mlsanity.com/paper/2306.05445/) (2023)
- [DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations](https://mlsanity.com/paper/2204.08672/) (2022)
- [Implicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular Dynamics](https://mlsanity.com/paper/2305.18046/) (2023)
- [Score-based denoising for atomic structure identification](https://mlsanity.com/paper/2212.02421/) (2022)
- [Accelerating discrete dislocation dynamics simulations with graph neural networks](https://mlsanity.com/paper/2208.03296/) (2022)

## Built on by (most cited first, 16 of 16)

- [Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials](https://mlsanity.com/paper/2410.01464/) (2024)
- [UniSim: A Unified Simulator for Time-Coarsened Dynamics of Biomolecules](https://mlsanity.com/paper/2506.03157/) (2025)
- [Force-Guided Bridge Matching for Full-Atom Time-Coarsened Dynamics of Peptides](https://mlsanity.com/paper/2408.15126/) (2024)
- [Sampling 3D Molecular Conformers with Diffusion Transformers](https://mlsanity.com/paper/2506.15378/) (2025)
- [HollowFlow: Efficient Sample Likelihood Evaluation using Hollow Message Passing](https://mlsanity.com/paper/2510.21542/) (2025)
- [A Comprehensive Survey on Diffusion Models and Their Applications](https://mlsanity.com/paper/2408.10207/) (2024)
- [JAMUN: Bridging Smoothed Molecular Dynamics and Score-Based Learning for Conformational Ensembles](https://mlsanity.com/paper/2410.14621/) (2024)
- [Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Space](https://mlsanity.com/paper/2509.02196/) (2025)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [TrustLDM: Benchmarking Trustworthiness in Language Diffusion Models](https://mlsanity.com/paper/2606.00023/) (2026)
- [Sifting through the Noise: A Survey of Diffusion Probabilistic Models and Their Applications to Biomolecules](https://mlsanity.com/paper/2406.01622/) (2024)
- [Grand canonical generative diffusion model for crystalline phases and grain boundaries](https://mlsanity.com/paper/2408.15601/) (2024)
- [ATOM: A Pretrained Neural Operator for Multitask Molecular Dynamics](https://mlsanity.com/paper/2510.05482/) (2025)
- [Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks](https://mlsanity.com/paper/2507.21763/) (2025)
- [Conditional Denoising Model as a Physical Surrogate Model](https://mlsanity.com/paper/2601.21021/) (2026)
- [Teaching Molecular Dynamics to a Non-Autoregressive Ionic Transport Predictor](https://mlsanity.com/paper/2605.09311/) (2026)

## Abstract (arXiv)

We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with respect to the dynamical degrees of freedom. The latter play the same role as force fields in MD but are used in denoising diffusion probability models to generate discrete transitions of the dynamical variables in an SD timestep, which can be orders of magnitude larger than a typical MD timestep. In this work, we construct graph neural network based score dynamics models of realistic molecular systems that are evolved with 10~ps timesteps. We demonstrate the efficacy of score dynamics with case studies of alanine dipeptide and short alkanes in aqueous solution. Both equilibrium predictions derived from the stationary distributions of the conditional probability and kinetic predictions for the transition rates and transition paths are in good agreement with MD. Our current SD implementation is about two orders of magnitude faster than the MD counterpart for the systems studied in this work. Open challenges and possible future remedies to improve score dynamics are also discussed.