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.
The paper investigates Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known only up to a normalisation constant. It demonstrates that for strongly log-concave targets satisfying certain curvature conditions, WFR flows preserve strong log-concavity—unlike pure Wasserstein flows, which only do so in the Gaussian case. Leveraging this property, the authors derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, showing an additive decomposition into Wasserstein and Fisher‑Rao contributions and eliminating the need for a warm start.
arXiv:2607. 07519v1 Announce Type: new Abstract: 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.
The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.
arXiv:2608. 07648v1 Announce Type: cross Abstract: Sampling high-dimensional probability distributions is a central task in scientific computing, with applications ranging from Bayesian inference to statistical physics and molecular simulation.
arXiv:2607. 10853v1 Announce Type: cross Abstract: Diffusion models faithfully reproduce their training distribution, but also inherit its imbalances and leave rare or under-represented modes hard to reach.
METALICA is a new method that combines Metadynamics with Replica Exchange on pretrained diffusion models to improve sampling of rare conformational states in proteins. It builds a bias potential along a chosen Collective Variable, pushes new samples away from previously visited ones, and reweights them to recover the unbiased distribution. By running one replica per diffusion level and allowing inter‑replica communication, METALICA can generate long Markov chains that uncover rare events, as demonstrated on a bimodal test system and on protein unfolding where it reveals a second free‑energy minimum that other methods miss.