Markov Chains and Monte Carlo Methods

Latest papers

• Posterior sampling by source-space MCMC via prior-based few-step transport maps

  Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian Wang · 2 October 2026

  Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, and pretrained generative models. The same computational problem appears in the test-time guidance task (generalized Bayes), where an explicit positive w…

• Learning Continuous Neural Representation of Stochastic Hybrid Systems

  Sangli Teng, Hang Liu, Koushil Sreenath · 1 October 2026

  A stochastic hybrid system (SHS) is governed by a stochastic differential equation (SDE) describing the continuous dynamics and a Markov reset kernel triggered on the guard surface. Its probability evolution can be described by a hybrid Fokker-Planck (HFP) equation with a partial differential term c…

• First-Order Stationarity of Reverse Diffusions

  Zhifeng Chen, Chenyang Jiang, Yazhen Wang · 28 September 2026

  Recent literature has shown a strong connection between optimization and sampling. We develop the corresponding first-order theory for diffusion models. First, the SDE-based reverse-time flows of overdamped and underdamped Langevin diffusions contract relative Fisher divergences at explicit exponent…

• Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding

  Yi Zhang, Rui Guo, Mengchu Xu, Zhaofeng Liu, Yonina C. Eldar · 28 September 2026

  Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hi…

• Nuclear Norm-Regularized Bayesian Matrix Completion

  Calvin Tolbert · 25 September 2026

  Matrix completion, the problem of estimating missing entries in a matrix from noisily observed ones, underlies a diverse array of problems such as recommender systems and counterfactual outcome estimation in panel data. Many algorithms address the problem using regularized least squares, often with …

• Neural Transport Nested Sampling

  David Yallup, Will Handley · 25 September 2026

  Sampling from Boltzmann distributions of molecular systems is an inference problem that has seen significant recent developments fuelled by advances in neural density estimation. We develop a novel sampling algorithm, Neural Transport Nested Sampling (NTNS), which combines the classical strengths of…

• Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler

  Stefan Oberd\"orster · 24 September 2026

  Local geometric mixing localizes geometric mixing by requiring geometric convergence to equilibrium in total variation only over finitely many transitions. It accommodates local convergence rates and captures rapid local equilibration, even when global mixing is much slower. We establish and discuss…

• Robustness of Diffusion Models under Distribution Shift

  Wei Luo, Neil K. Chada, Shijie Zhang, Lu Yu · 24 September 2026

  Score-based diffusion models are increasingly considered in settings where the underlying data distribution may differ from the training distribution, yet existing theoretical guarantees largely focus on the no-shift setting. In this work, we study robust score estimation under Wasserstein perturbat…

• Penalized Nonreversible Langevin for Constrained Sampling

  Pervez Ali, Weihao Dong, Xiaoyu Wang · 23 September 2026

  We propose penalized nonreversible Langevin algorithms for sampling from $\pi(x)\propto e^{-f(x)}\mathbf 1_{\mathcal C}(x)$, where $\mathcal C\subset\mathbb R^d$ is a compact convex set. The algorithms combine a squared distance penalty with constant or compatible state dependent skew symmetric pert…

• Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplers

  Jian Xu · 23 September 2026

  Neural samplers are trained against an unnormalised target $\tilde\pi=e^{-E}$ with no samples from $\pi$, which leaves the practitioner with no way to tell whether an expensive training run has silently dropped part of the target. The diagnostics in common use are computed from the model's own draws…

• Gaussian Flow-Matching Schedules: Implications for Sampling and Training

  Ars\`ene Claustre (DI-ENS), Hugo Negrel (DMA, CFM), Claire Boyer (LMO, IUF), Kimia Nadjahi (DI-ENS), Eric Vanden-Eijnden (DMA, CFM, CIMS) · 23 September 2026

  Flow-matching schedules affect both sampling dynamics and the variance of the regression target. For centered commuting Gaussians, we show that a direction-dependent schedule decomposes into two independent design choices: a variance path, which fully determines the intermediate laws and probability…

• Accelerating Diffusion Sampling via Speculative Draft Trees

  Marcello Bullo, Yanxiao Liu, \"Oyk\"u S{\i}la G\"uner, Arpan Mukherjee, Deniz G\"und\"uz · 17 September 2026

  Speculative sampling accelerates diffusion model generation by drafting inexpensive candidate states and correcting them under a coupling that preserves the target distribution exactly, reducing the number of expensive target evaluations. Existing diffusion samplers, notably those based on reflectio…

• Tight Sampling Complexity with stochastic gradient oracles in Fixed Dimensions

  Weiming Ou, Xiao Wang · 14 September 2026

  We investigate the stochastic-gradient query complexity of sampling smooth strongly log-concave distributions in any fixed Euclidean dimension. The potential is $\mu$-strongly convex and $L$-smooth, with an unknown mode in the ball of radius $\mu^{-1/2}$ about the origin. We have access to unbiased …

• A Splitting Method for SDE Terminal-Law Estimation

  Rushil Gupta, Sandeep Juneja · 14 September 2026

  In many settings involving stochastic differential equations, including in diffusion based generative AI, our aim is to accurately generate samples from a terminal distribution. Typically, this is done by generating i.i.d. samples of diffusion paths. Given a fixed simulation budget, a reasonable way…

• Poisson-Corrector Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling

  Yuchen Xin, Zhihua Zhang · 14 September 2026

  We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz. For t…

• Score-based Outlier Generation via Controlling the Radon-Nikodym Derivative

  Amartya Mukherjee, Tristan Milne, Kry Yik-Chau Lui, Stephanie Hazlewood, Jun Liu · 14 September 2026

  Outliers are important for stress-testing algorithms and understanding system behaviour under rare conditions. Despite being commonly described as low-likelihood events, existing generative approaches rarely control likelihood explicitly. In this work, we introduce a measure-theoretic notion of outl…

• Deep operator learning for efficient sampling from invariant measures of stochastic differential equations

  Lin Guo, Li Lei, Jingtong Zhang · 11 September 2026

  We introduce an amortized neural sampler that combines operator learning with flow methods for sampling. It maps SDE coefficient functions to pushforwards from a reference measure to the invariant measures, enabling efficient sampling across families of stochastic differential equations. Our framewo…

• Particle GFlowNets: Rethinking Generative Marginalization Models

  Tiago da Silva, Diego Mesquita, Salem Lahlou · 11 September 2026

  Generative Marginalization Models (MaMs) have been recently introduced as efficient neural sampling models for any-order autoregressive modelling of discrete distributions. By learning both the marginal and conditional probabilities of a persistent-block Gibbs sampler, MaMs enable fast posterior eva…

• Gaussian Approximation for Multivariate Martingale Sums from Uniformly Ergodic Markov Chains

  Yixuan Zhang, Qiaomin Xie · 10 September 2026

  We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences generated by a uniformly ergodic Markov chain. Under an $L^{(2+\eta)p}$-moment condition with $\eta>0$, we establish the explicit bound $$ O\left( p^3 \|A\|_…

• Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation

  Qi Feng, Rongjie Lai, Di Qi, Xuda Ye · 10 September 2026

  Normalizing flow Boltzmann generators retain a tractable pushforward density, but training with forward KL depends on target samples that may be biased or omit modes. As a result, a flow can miss target mass while its observed importance weights give a high effective sample size. We introduce the lo…

• Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference

  Heinrich von Campe, Bjoern Malte Schaefer · 9 September 2026

  The concept of Markov chain Monte Carlo (MCMC) cycles, an analogy to cyclic processes in heat engines, is presented in order to examine Bayesian inference problems. In this effort, we develop adaptive ensemble schedulers that allow the tuning of external parameters of a Bayesian canonical ensemble d…

• Microcanonical Hamiltonian Monte Carlo and the Helmholtz Theorem

  Heinrich von Campe, Bjoern Malte Schaefer · 9 September 2026

  The recently proposed Microcanonical Hamiltonian Monte Carlo algorithm has not yet been studied in detail from a thermodynamic point of view; this work aims to fill that gap. We demonstrate how thermodynamical state variables and potentials can be derived and thereby demonstrate that the constructio…

• FrOGS: Discrete Neural Sampler for Independent Alloy Configurations Across Chemical Conditions

  Kyucheol Min, Elyssa Hofgard, Tess Smidt · 4 September 2026

  Predicting the thermodynamic properties of an alloy requires sampling its configurations across many chemical conditions and recovering free energies on a common absolute scale. Markov chain Monte Carlo (MCMC) is the standard tool, but it requires separate simulations at different conditions, and au…

• Schr\"odinger Bridges on Lie Group Manifolds for Probabilistic Intrinsic Generation

  Shizhe Zhang, Mingyang Zhao, Lei Ma · 3 September 2026

  Generative modeling directly on geometric manifolds can avoid errors introduced by flattening non-Euclidean data, repeated ambient projection, and coordinate inconsistency in Euclidean representations. Schrodinger bridges provide a probabilistic generative framework for entropy-regularized transport…

• Exact Global MCMC with Denoising Diffusion

  Mitch Hill · 2 September 2026

  This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional target densities. The method is motivated by the observation that sequentially applying a forward and reverse diffusion process defines a Markov chain w…