{"paper":{"title":"Proximal-Based Generative Modeling for Bayesian Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"PGM replaces the intractable likelihood score in diffusion models with a closed-form Moreau score computed via proximal operators, enabling non-asymptotic sampling for inverse problems trained only on prior data.","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Boyang Zhang, Ya-Feng Liu, Zhiguo Wang","submitted_at":"2026-05-13T09:55:51Z","abstract_excerpt":"Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we propose a novel proximal-based generative modeling (PGM) framework that rigorously circumvents explicit likelihood evaluation. Our framework is built upon a theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization in nonsmooth optimization. This enables a new sampling mechanism driven by the proposed Moreau"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"PGM eliminates the early-stopping bias inherent in the score-based diffusion model and achieves non-asymptotic convergence.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization holds rigorously and directly yields a closed-form Moreau score via proximal operators that can be learned from prior samples alone.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"PGM replaces the intractable likelihood score in diffusion models with a closed-form Moreau score computed via proximal operators, enabling non-asymptotic sampling for inverse problems trained only on prior data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"812e48c6a30d14e698b30942c9a5ff71c5427a112253e05ede842e249a5f690b"},"source":{"id":"2605.13278","kind":"arxiv","version":1},"verdict":{"id":"0b6aaa16-e9cc-421b-a4c9-298036a1975c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:50:32.559283Z","strongest_claim":"PGM eliminates the early-stopping bias inherent in the score-based diffusion model and achieves non-asymptotic convergence.","one_line_summary":"PGM replaces the intractable likelihood score in diffusion models with a closed-form Moreau score computed via proximal operators, enabling non-asymptotic sampling for inverse problems trained only on prior data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization holds rigorously and directly yields a closed-form Moreau score via proximal operators that can be learned from prior samples alone.","pith_extraction_headline":""},"references":{"count":132,"sample":[{"doi":"","year":null,"title":"Proceedings of the 28th International Conference on Machine Learning , pages=","work_id":"f56af9f4-6863-41d7-ad3d-428f36b0db8d","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Score-Based Generative Modeling through Stochastic Differential Equations","work_id":"d9110e53-a5d4-4794-a4c5-a575e91c31ad","ref_index":2,"cited_arxiv_id":"2011.13456","is_internal_anchor":true},{"doi":"","year":2022,"title":"SIAM Review , volume=","work_id":"407f94c0-e357-481c-a896-7a93b1dffbcd","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Advances in Neural Information Processing Systems , volume=","work_id":"49d8a4df-67bb-49cb-9185-1d7d846f43ae","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Statistical Physics: Volume 5 , author=. 2013 , publisher=","work_id":"da20961b-d717-455a-a320-d4d40b10b949","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":132,"snapshot_sha256":"042b6f153dbb9b54717acde1afeb0afd7fc65644f0294852322a009eea13d7d6","internal_anchors":5},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}