Michael Plainer

@plainer.bsky.social

90 Followers 47 Following

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

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.
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.
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.
Animation showing the two modes of our model: independent sampling by diffusion denoising (left) and molecular dynamics simulation (right).