Data to 7 Oct 2026

Elements of Sequential Monte Carlo

arXiv 1903.04797 ↗First posted 12 Mar 2019stat.ML cs.LG stat.COcited by 60

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Abstract (arXiv)

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.

Key facts. Cited by 60 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Mar 2019.

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Citing papers per year: 2021: 6; 2022: 6; 2023: 5; 2024: 9; 2025: 18; 2026: 16.

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2021GFlowNet Foundationscited by 286
2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
2025Test-time Alignment of Diffusion Models without Reward Over-optimizationcited by 89
2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
2025Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlocited by 45
2022A Variational Perspective on Generative Flow Networkscited by 39
2022SIXO: Smoothing Inference with Twisted Objectivescited by 22
2021A Probabilistic State Space Model for Joint Inference from Differential Equations and Datacited by 21
2024Step-by-Step Reasoning for Math Problems via Twisted Sequential Monte Carlocited by 21
2025Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Designcited by 21
2025Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Samplingcited by 20

38 more

2025SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationscited by 19
2021Nested Variational Inferencecited by 14
2022BR-SNIS: Bias Reduced Self-Normalized Importance Samplingcited by 12
2021Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inferencecited by 10
2026A Probabilistic Framework for LLM-Based Model Discoverycited by 10
2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlocited by 9
2022Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transportcited by 8
2024Sequential Monte Carlo for Inclusive KL Minimization in Amortized Variational Inferencecited by 7
2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlocited by 7
2025Inference-Time Scaling of Diffusion Language Models via Trajectory Refinementcited by 7
2025MIRA: Towards Mitigating Reward Hacking in Inference-Time Alignment of T2I Diffusion Modelscited by 7
2021Learning Proposals for Probabilistic Programs with Inference Combinatorscited by 6
2021Variational Marginal Particle Filterscited by 6
2026Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world modelscited by 6
2023Discriminator Guidance for Autoregressive Diffusion Modelscited by 5
2024PASOA- PArticle baSed Bayesian Optimal Adaptive designcited by 5
2025Trust-Region Twisted Policy Improvementcited by 5
2025Reinforced sequential Monte Carlo for amortised samplingcited by 5
2022Black-box Coreset Variational Inferencecited by 4
2023Sparse Graphical Linear Dynamical Systemscited by 4
2023NAS-X: Neural Adaptive Smoothing via Twistingcited by 4
2024Probabilistic Programming with Programmable Variational Inferencecited by 4
2026Particle-Guided Diffusion Models for Partial Differential Equationscited by 4
2025ProSpero: Active Learning for Robust Protein Design Beyond Wild-Type Neighborhoodscited by 3
2025DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolantscited by 3
2026Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Designcited by 3
2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 3
2024Lifelong Learning of Video Diffusion Models From a Single Video Streamcited by 2
2025Deep Variational Sequential Monte Carlo for High-Dimensional Observationscited by 2
2024On the connection between Noise-Contrastive Estimation and Contrastive Divergencecited by 1
2024VISA: Variational Inference with Sequential Sample-Average Approximationscited by 1
2024Variational Pseudo Marginal Methods for Jet Reconstruction in Particle Physicscited by 1
2026Discrete Diffusion Inference-Time Control with Nested Sequential Monte Carlocited by 1
2022Marginalized particle Gibbs for multiple state-space models coupled through shared parameterscited by 0
2023String Diagrams with Factorized Densitiescited by 0
2025Preference Optimization via Contrastive Divergence: Your Reward Model is Secretly an NLL Estimatorcited by 0
2025A State-Space Approach to Nonstationary Discriminant Analysiscited by 0
2025Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Spacecited by 0

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