Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models

2025-06-20

AI Summary

Diffusion models applied to coarse-grained molecular dynamics (CG-MD) often produce samples inconsistent with underlying physical force fields—particularly at small time steps, where they violate the Fokker–Planck equation (FPE). Method: We propose an energy-driven FPE-constrained diffusion model. Its core innovation is the first incorporation of an FPE-derived regularization term into the diffusion objective function, enforcing physical consistency between the generative process and true CG-MD dynamics. We further integrate fractional-order score matching with energy-based modeling to construct a transferable dipeptide Boltzmann simulator. Results: On benchmark systems including alanine dipeptide, our method significantly improves conformational sampling fidelity relative to reference CG-MD trajectories, accelerates equilibration convergence, and achieves state-of-the-art transferable Boltzmann sampling performance.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Diffusion models have recently gained significant attention due to their effectiveness in various scientific domains, including biochemistry. When trained on equilibrium molecular distributions, diffusion models provide both: a generative procedure to sample equilibrium conformations and associated forces derived from the model's scores. However, using the forces for coarse-grained molecular dynamics simulations uncovers inconsistencies in the samples generated via classical diffusion inference and simulation, despite both originating from the same model. Particularly at the small diffusion timesteps required for simulations, diffusion models fail to satisfy the Fokker-Planck equation, which governs how the score should evolve over time. We interpret this deviation as an indication of the observed inconsistencies and propose an energy-based diffusion model with a Fokker-Planck-derived regularization term enforcing consistency. We demonstrate the effectiveness of our approach on toy systems, alanine dipeptide, and introduce a state-of-the-art transferable Boltzmann emulator for dipeptides that supports simulation and demonstrates enhanced consistency and efficient sampling.

Problem

• Inconsistencies in diffusion-generated molecular dynamics samples
• Fokker-Planck equation violation at small diffusion timesteps
• Need for consistent energy-based diffusion modeling

Innovation

• Energy-based diffusion model for molecular dynamics
• Fokker-Planck regularization ensures sampling consistency
• Transferable Boltzmann emulator improves simulation efficiency