Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling

arXiv:2610.02081 · stat.ML, cs.LG, math-ph, math.DS, math.MP, math.PR, math.SP · Submitted 2026-10-01 · Read on arXiv

stat.ML, cs.LG, math-ph, math.DS, math.MP, math.PR, math.SP

Submitted: 2026-10-01

Updated: 2026-10-01

Terminology

• Gradient Flow — 21× in this paper · explained in 2 episodes
• Spectral Gap — 8× in this paper · explained in 5 episodes
• Diffusion Processes — 7× in this paper · explained in 2 episodes
• Langevin Dynamics — 7× in this paper · explained in 2 episodes
• Metastability — 7× in this paper · explained in 2 episodes
• Optimal Transport — 6× in this paper · explained in 5 episodes
• Bayesian Inference — 3× in this paper · explained in 5 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Denoising Diffusion Sampler — 2× in this paper
• Los Alamos National Laboratory — 2× in this paper
• Path Integral Sampler — 2× in this paper
• Score Function — 2× in this paper · explained in 4 episodes
• Theoretical Guarantees — 2× in this paper · explained in 2 episodes
• Variational Wasserstein Gradient Flow — 2× in this paper
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Laboratory Directed Research and Development — 1× in this paper
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Stochastic Dynamics — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• MCMC using Hamiltonian dynamics
• Challenges for quantum computation of nonlinear dynamical systems using linear representations

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