Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling
Read the original on arXiv Statistics ML →The Flow has not summarised this story yet — read it at arXiv Statistics ML.
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arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
arXiv:2602. 16634v2 Announce Type: replace-cross Abstract: The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation.
arXiv:2601. 21026v2 Announce Type: replace-cross Abstract: Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics.
The paper introduces a new Markov chain Monte Carlo method that samples from multimodal distributions by interpolating along the diffusion path of a noising diffusion process, preserving mode weights and improving mixing. It proposes a Metropolis-adjusted diffusion path (MAD-Path) sampler that corrects for bias from approximate score estimates and discretization errors, ensuring the target distribution remains invariant. Experiments on Bayesian posteriors demonstrate that MAD-Path outperforms tempering-based MCMC and unadjusted diffusion samplers in global exploration and accurate mode-weight estimation.
We address the problem of efficiently sampling multimodal probability distributions, where standard Markov Chain Monte Carlo methods often suffer from poor mixing and mode trapping. To mitigate these issues, we propose Gradient-free Riemannian Langevin Sampler (GRiLS), a novel proposal that improves exploration without requiring gradient evaluations of the target density.
arXiv:2601. 08527v3 Announce Type: replace-cross Abstract: We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants.