The　interaction　data　used　by　recommender　systems　(RSs)　inevitably　include　noises　resulting　from　mistaken　or　exploratory　clicks,　especially　under　implicit　feedbacks.　Without　proper　denoising,　RS　models　cannot　effectively　capture　users’　intrinsic　preferences　and　the　true　interactions　between　users　and　items.　To　address　such　noises,　existing　methods　mostly　rely　on　auxiliary　data　which　are　not　always　available.　In　this　work,　we　ground　on　Optimal　Transport　(OT)　to　globally　match　a　user　embedding　space　and　an　item　embedding　space,　allowing　both　non-deep　and　deep　RS　models　to　discriminate　intrinsic　and　noisy　interactions　without　supervision.　Specifically,　we　firstly　leverage　the　OT　framework　via　Sinkhorn　distance　to　compute　the　continuous　many-to-many　user-item　matching　scores.　Then,　we　relax　the　regularization　in　Sinkhorn　distance　to　achieve　a　closed-form　solution　with　a　reduced　time　complexity.　Finally,　to　consider　individual　user　behaviors　for　denoising,　we　develop　a　partial　OT　framework　to　adaptively　relabel　user-item　interactions　through　a　personalized　thresholding　mechanism.　Extensive　experiments　show　that　our　framework　can　significantly　boost　the　performances　of　existing　RS　models.　©　2022　Copyright　for　this　paper　by　its　authors.