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Michael Plainer

@plainer.bsky.social

PhD student @ ELIZA TU/FU Berlin - plainer.dev

Michael Plainer @plainer.bsky.social · 06/11/2025

(5/n) With this, we can run coarse-grained Langevin dynamics directly, without the need for any priors or force labels. This works across biomolecular systems including fast-folding proteins like Chignolin and BBA. Here is a comparison with and without our regularization:

Comparison of equilibrium distributions obtained by iid sampling and Langevin simulation (sim) across different systems and methods. While classical iid sampling recovers the reference equilibrium distribution,
performing simulation with the learned score reveals inconsistencies when models are not trained with Fokker-Planck regularization, i.e., p(x) != p_0(x). Regularized models achieve consistent behavior across systems.

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Michael Plainer @plainer.bsky.social · 06/11/2025

(4/n) Our solution: We train an energy-based diffusion model and regularize it to satisfy the Fokker–Planck equation. This enforces consistency between: - The density recovered via denoising - The potential energy learned at t = 0 Result: the same model can be used for sampling AND simulation.

A model trained with Fokker–Planck regularization is self-consistent, and aligns the learned score at t = 0 with the distribution recovered by diffusion sampling.

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Michael Plainer @plainer.bsky.social · 06/11/2025

(2/n) The problem: classical diffusion models learn scores that reproduce equilibrium samples, but the corresponding energy-based parameterization is not consistent. So if you try to use the learned energy to derive forces, the dynamics are wrong, even if the samples themselves look fine.

Training diffusion models on a 2D toy example reveals inconsistencies. While classical iid diffusion sampling (i.e., denoising) correctly reproduces both modes, evaluating the score at t = 0 to estimate the unnormalized density yields a third mode and an incorrect mass distribution. Such a diffusion model would produce incorrect dynamics while producing correct samples.

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Michael Plainer @plainer.bsky.social · 06/11/2025

(1/n) Can diffusion models simulate molecular dynamics instead of just generating independent samples? In our NeurIPS 2025 paper, we train energy-based diffusion models that can do both: - Generate independent samples - Learn the underlying potential 𝑼 🧵👇 Paper: arxiv.org/abs/2506.17139

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