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We observe that the extinction gradients split into two components on structurally different integration domains: a scattering term evaluated at a single path vertex, and a transmittance term integrated along the ray segment. Because the domains are mismatched, existing estimators sample the two components at different locations, leaving the negative correlation between their opposite-signed contributions unexploited. We expose this overlooked correlation and exploit it through a principle we call\n                    <jats:italic toggle=\"yes\">sample matching<\/jats:italic>\n                    : evaluate both components at shared sample locations. To enable this, we derive the first reformulation of the differential path integral that couples the two contributions within a single integrand, yielding an unbiased Monte Carlo estimator that ties them together by construction. For efficiency, the estimator reuses partially sampled light paths and amortizes in-scattering cost by evaluating gradients at multiple probe points per segment. On voxel-grid reconstruction, our estimator reduces gradient variance by up to 80% over differential ratio tracking (DRT), yielding faster convergence and higher reconstruction quality.\n                  <\/jats:p>","DOI":"10.1145\/3811329","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Sample Matching for Joint Extinction Gradient Estimation in Differentiable Volume Rendering"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7057-985X","authenticated-orcid":false,"given":"Ruihan","family":"Yu","sequence":"first","affiliation":[{"name":"The University of Tokyo, Tokyo, Japan"},{"name":"Tsinghua University, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8518-5486","authenticated-orcid":false,"given":"Yu-Chen","family":"Wang","sequence":"additional","affiliation":[{"name":"University of California Irvine, Irvine, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8746-8578","authenticated-orcid":false,"given":"Jingwang","family":"Ling","sequence":"additional","affiliation":[{"name":"University of Illinois Urbana-Champaign, Champaign, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0953-1057","authenticated-orcid":false,"given":"Feng","family":"Xu","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4759-0514","authenticated-orcid":false,"given":"Shuang","family":"Zhao","sequence":"additional","affiliation":[{"name":"University of Illinois Urbana-Champaign, Champaign, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3648611"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.112.2096"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14956"},{"key":"e_1_2_2_4_1","volume-title":"Radiative Transfer","author":"Chandrasekhar Subrahmanyan","year":"1950","unstructured":"Subrahmanyan Chandrasekhar. 1960. 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