{"paper":{"title":"Reasoning on the Manifold: Bidirectional Consistency for Self-Verification in Diffusion Language Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Diffusion language models can verify their own reasoning by measuring how stable generated sequences remain under a forward-masking and backward-reconstruction cycle on the learned manifold.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Guanghao Li, Hengyu Zeng, Jian Pu, Jiaoyang Ruan, Jie Fu, Liang Du, Xin Gao, Yinda Chen","submitted_at":"2026-04-17T10:17:16Z","abstract_excerpt":"While Diffusion Large Language Models (dLLMs) offer structural advantages for global planning, efficiently verifying that they arrive at correct answers via valid reasoning traces remains a critical challenge. In this work, we propose a geometric perspective: Reasoning on the Manifold. We hypothesize that valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, whereas invalid paths exhibit off-manifold drift. To operationalize this, we introduce Bidirectional Manifold Consistency (BMC), a training-free, unsupervised metric that quanti"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, and the forward-masking backward-reconstruction cycle accurately quantifies this stability as a proxy for correctness.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Bidirectional Manifold Consistency (BMC) is a geometric, training-free metric that quantifies stability of reasoning trajectories in diffusion LLMs to enable self-verification, rejection sampling, and alignment without ground truth.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Diffusion language models can verify their own reasoning by measuring how stable generated sequences remain under a forward-masking and backward-reconstruction cycle on the learned manifold.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f3c344123a4bed2cb2f1935ce15b3a193caac0151ee6211307b27f51c9ef361c"},"source":{"id":"2604.16565","kind":"arxiv","version":3},"verdict":{"id":"9e1bc318-cdf3-4987-8c35-2bf311695f33","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T08:42:15.048118Z","strongest_claim":"Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.","one_line_summary":"Bidirectional Manifold Consistency (BMC) is a geometric, training-free metric that quantifies stability of reasoning trajectories in diffusion LLMs to enable self-verification, rejection sampling, and alignment without ground truth.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, and the forward-masking backward-reconstruction cycle accurately quantifies this stability as a proxy for correctness.","pith_extraction_headline":"Diffusion language models can verify their own reasoning by measuring how stable generated sequences remain under a forward-masking and backward-reconstruction cycle on the learned manifold."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16565/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}