Diffusion Models are Molecular Dynamics Simulators

Justin Diamond, Markus Alexander Lill

Keywords: Diffusion, molecular dyanmics, generation, trajectories

Abstract:

We prove an exact equivalence: a denoising–diffusion sampler augmented with a harmonic adapter—a quadratic, offset coupling that links successive reverse‑time iterates—is precisely the Euler–Maruyama integrator for overdamped Langevin dynamics. A single reverse step with spring stiffness k integrates the SDE with an implicit step size equal to beta divided by two times k; the drift term is the learned score (i.e., the gradient of the learned energy). This identity reframes molecular dynamics through diffusion: the fidelity of both trajectories and equilibrium statistics is governed by two knobs—model capacity (via universal approximation of the drift) and the number of denoising steps N—rather than by a fixed, vanishingly small MD time step.

Practically, this yields a data‑driven MD pipeline that learns forces directly from independent and identically distributed configurations, needs no hand‑crafted force fields, and can run in a small, distillable number of reverse steps while preserving the Boltzmann distribution induced by the learned energy. We establish pathwise Kullback–Leibler bounds that separate discretization error—scaling with the sum of squared step sizes—from score error, clarify how temperature enters through the spring (beta is the inverse temperature, so the effective step size is set by the ratio of beta to k), and demonstrate MD‑like temporal correlations in trajectories generated entirely by a score model trained on static samples.

Primary Area: generative models

Submission Number: 3451