{"paper":{"title":"Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A landing mechanism enables efficient diffusion models on nonconvex sets by replacing costly projections with a single-step correction.","cross_cats":["stat.CO","stat.ML"],"primary_cat":"cs.LG","authors_text":"Kijung Jeon, Michael Muehlebach, Molei Tao","submitted_at":"2026-04-20T05:47:27Z","abstract_excerpt":"Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets $\\Sigma$ that simultaneously enforces equality and inequality constraints throughout the diffusion process. Our framework incorporates both overdamped and underdamped dynamics for forward and backward sampling. A key algorithmic innovation is a computationally efficient landing mechanism that replaces cos"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto Σ, ensuring feasibility without iterative Newton solves or projection failures.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The landing mechanism works for generic nonconvex feasible sets Σ and preserves the correct diffusion dynamics without introducing bias or instability.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A landing algorithm lets diffusion models sample from nonconvex constrained sets using underdamped dynamics without repeated projections or Newton solves.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A landing mechanism enables efficient diffusion models on nonconvex sets by replacing costly projections with a single-step correction.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"11e80eacb8ebf5f245249de43ef5fe2592d099e51bee4c50a44a48c8510d7a28"},"source":{"id":"2604.17838","kind":"arxiv","version":2},"verdict":{"id":"35494912-8e7a-444f-9a80-3f0efc107625","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T05:51:06.694675Z","strongest_claim":"A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto Σ, ensuring feasibility without iterative Newton solves or projection failures.","one_line_summary":"A landing algorithm lets diffusion models sample from nonconvex constrained sets using underdamped dynamics without repeated projections or Newton solves.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The landing mechanism works for generic nonconvex feasible sets Σ and preserves the correct diffusion dynamics without introducing bias or instability.","pith_extraction_headline":"A landing mechanism enables efficient diffusion models on nonconvex sets by replacing costly projections with a single-step correction."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.17838/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T04:42:19.839387Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"94825b64b708e2ebcf26014f2cc38859f2107c7b22742f178bb71d2b4a5ded1e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"}