{"doi":"10.1098/rsta.2024.0331","title":"Bridging diffusion posterior sampling and Monte Carlo methods: a survey","abstract":"<jats:p>\n                    Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modelling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage\n                    <jats:italic toggle=\"yes\">pre-trained</jats:italic>\n                    diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a\n                    <jats:italic toggle=\"yes\">twisting</jats:italic>\n                    mechanism for the intermediate distributions within the diffusion process, guiding the simulations towards the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.\n                  </jats:p>\n                  <jats:p>This article is part of the theme issue ‘Generative modelling meets Bayesian inference: a new paradigm for inverse problems’.</jats:p>","journal":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","year":2025,"id":617948,"datarank":0.10397207708399181,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"self_citation_contribution":0.10397207708399181,"citation_network_contribution":0.0,"self_endowment_contribution":0.10397207708399181,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1593814,"name":"Eric Moulines","orcid":"0000-0002-2058-0693","position":1,"is_corresponding":false},{"id":1593816,"name":"Jimmy Olsson","orcid":null,"position":2,"is_corresponding":false},{"id":1593817,"name":"Alain Oliviero-Durmus","orcid":null,"position":3,"is_corresponding":false},{"id":1593813,"name":"Yazid Janati","orcid":"0000-0002-7271-4104","position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Bridging diffusion posterior sampling and Monte Carlo methods: a survey","abstract":"<jats:p>\n                    Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modelling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage\n                    <jats:italic toggle=\"yes\">pre-trained</jats:italic>\n                    diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a\n                    <jats:italic toggle=\"yes\">twisting</jats:italic>\n                    mechanism for the intermediate distributions within the diffusion process, guiding the simulations towards the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.\n                  </jats:p>\n                  <jats:p>This article is part of the theme issue ‘Generative modelling meets Bayesian inference: a new paradigm for inverse problems’.</jats:p>","is_dataset_classified":null,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"40534298","pmcid":null,"openalex_id":"https://openalex.org/W4411469233","authors":[],"funders":[],"total_grants":0,"fwci":1.2699,"citation_percentile":0.84316181,"influential_citations":0,"citation_trend":[{"year":2026,"count":1}],"oa_status":"closed","license":"https://royalsociety.org/-/media/journals/author/Licence-to-Publish-20062019-final.pdf","oa_locations":[{"url":"https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2024.0331","host_type":"publisher"},{"url":"https://royalsocietypublishing.org/doi/full-xml/10.1098/rsta.2024.0331","host_type":"publisher"},{"url":"https://doi.org/10.1098/rsta.2024.0331","host_type":"journal"},{"url":"https://pubmed.ncbi.nlm.nih.gov/40534298","host_type":"repository"}],"fields_of_study":["Bayesian Methods and Mixture Models","Markov Chains and Monte Carlo Methods","Advanced Neuroimaging Techniques and Applications"],"mesh_terms":[],"keywords":["Markov chain Monte Carlo","Computer science","Monte Carlo method","Prior probability","Bayesian probability","Bayesian inference","Leverage (statistics)","Importance sampling","Bridging (networking)","Inference","Posterior probability","Particle filter","Generative grammar","Inverse problem","Algorithm","Artificial intelligence","Statistical physics","Mathematics","Statistics","Physics","Monte Carlo Methods","Diffusion Models","Bayesian Inverse Problems"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-03T03:02:32.519545Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}