Multimodal Distribution Sampling

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Transport along Local Annealing Paths: Wasserstein Geometry and Multimodal Sampling
Nov 3, 2026Han Chen, Sifan LiuMultimodal Distribution Sampling Optimal Transport
Department of Statistical Science, Duke University
Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling
Oct 1, 2026Daniel McBride, Pratik Khandagale, Cristina Garcia-Cardona +1Dynamical Systems Wasserstein Gradient Flows
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Nonlocal Hamiltonian Dynamics on Sparse Lévy Graphs: Spectral Analysis and Multimodal Sampling
Oct 1, 2026Miaolei Zheng, Ting Gao, Jinqiao DuanMultimodal Distribution Sampling Hamiltonian Dynamics
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China · School of Sciences, Great Bay University, Dongguan 523000, China · Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems, Great Bay University, Dongguan 523000, China +3
Gradient-free Riemannian Langevin Sampler
Jul 8, 2026Ricardo Baptista, Olivier ZahmMarkov Chain Monte Carlo Multimodal Distribution Sampling
Department of Statistical Sciences, University of Toronto, Canada · UGA, Inria, CNRS, Grenoble INP*, LJK, 38000 Grenoble, France
Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging
Apr 12, 2026Pinaki Mohanty, Ruqi ZhangMultimodal Distribution Sampling Markov Chain Monte Carlo
Department of Computer Science, College of Science & College of Engineering, Purdue University, West Lafayette, IN, USA
Sampling from multimodal distributions with warm starts: Non-asymptotic bounds for the Reweighted Annealed Leap-Point Sampler
Dec 19, 2025Holden Lee, Matheau Santana-GijzenMultimodal Distribution Sampling Markov Chain Monte Carlo
Bouncy particle sampler with infinite exchanging parallel tempering
Sep 2, 2025Yohei Saito, Shun Kimura, Koujin TakedaMultimodal Distribution Sampling Markov Chain Monte Carlo
Center for Mathematics and Data Science, Gunma University · Graduate School of Science and Engineering, Ibaraki University
Interacting Annealed Importance Sampling via Population-Based MCMC Kernels
Jan 28, 2024Haoxuan Chen, Lexing YingMultimodal Distribution Sampling Importance Sampling
Institute for Computational and Mathematical Engineering (ICME), Stanford University, Stanford, CA, 94305, USA · Department of Mathematics and Institute for Computational and Mathematical Engineering (ICME), Stanford University, Stanford, CA, 94305, USA

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Transport along Local Annealing Paths: Wasserstein Geometry and Multimodal Sampling

Han Chen, Sifan Liu

Department of Statistical Science, Duke University

Multimodal Distribution Sampling Optimal Transport

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Variational approaches to learning transport maps for multimodal sampling can suffer from mode collapse. One way to mitigate this problem is to learn transport along a prescribed path of intermediate distributions defined by geometric annealing. We show that annealing can take a substantial detour in Wasserstein space: when mass moves between modes, the path can be much longer than the distance between its endpoints. We further link path geometry to transport learning, showing that long annealing paths can slow population optimization, while sufficiently regular paths permit rapid convergence. Motivated by these findings, we propose componentwise annealed transport (CAT) to reduce the need for mass transfer between modes. Starting from a mode-informed mixture reference, CAT constructs an exact mixture decomposition of the target and learns separate transport maps along componentwise annealing paths. We estimate the component weights separately and show that these estimates remain consistent even when the learned flows are inexact. We also develop adaptive annealing schedules guided by transport effort. Experiments on multimodal synthetic distributions and Bayesian inference problems demonstrate improvements in transport learning and sampling efficiency.