Rituxan/BEAM vs Bexxar/BEAM in Autologous Hematopoietic Stem Cell Transplant for Non-Hodgkin's Lymphoma (BMTCTN0401)

Inclusion Criteria: * Diagnosis of persistent or recurrent REAL classification diffuse large B-cell lymphoma, composite lymphoma with more than 50% diffuse large B-cell lymphoma, mediastinal B-cell lymphoma * Demonstration of CD20+ on at least one histologic specimen * 18-80 years old at time of first registration * Three or fewer prior regimens of chemotherapy over the entire course of their disease treatment (including one induction chemotherapy and no more than 2 salvage chemotherapies); monoclonal antibody therapy and involved field radiation therapy will not be counted as prior therapies * Disease status of primary induction failure, first relapse, or second complete remission; all patients must have chemosensitive disease as demonstrated by response to induction or salvage chemotherapy with at least a partial response (as defined in the protocol) * No more than a 20% bone marrow involvement * Patients with adequate organ function as measured by: * Cardiac: American Heart Association Class I: Patients with cardiac disease but without resulting limitation of physical activity; ordinary physical activity does not cause undue fatigue, palpitation, dyspnea, or anginal pain; additionally, patients greater than 60 years of age must have a left ventricular ejection fraction at rest of at least 40% demonstrated by Multi-Gated Acquisition Scan (MUGA) * Hepatic: Bilirubin less than 2.0 mg/dL (except for isolated hyperbilirubinemia attributed to Gilbert syndrome) and alanine transaminase (ALT) and aspartate transaminase (AST) less than 3x the upper limit of normal * Renal: Creatinine less than 2.0 mg/dL or creatinine clearance (calculated creatinine clearance is permitted) more than 40 mL/min; no hydronephrosis on CT scan prior to mobilization * Pulmonary: Carbon Monoxide Diffusing Capacity (DLCO), Volume forcibly exhaled in one second (FEV1), forced vital capacity (FVC) at least 45% of predicted (corrected for hemoglobin) * Autologous graft with a minimum of at least 1.5 X 10\^6 CD34+ cells/kg (target greater than 2.0 X 10\^6 CD34+ cells/kg. Peripheral blood stem cells (PBSC) are preferred; however, if PBSC mobilization fails, cells can be obtained by institutional practices (in cases where bone marrow will be used for transplantation, the required CD34+ dose does not apply and institutional practice for total nucleated cell dose should be used). * Initiate conditioning therapy within 3 months of mobilization * Signed informed consent Exclusion Criteria: * Karnofsky performance score less than 70% * Transformed follicular lymphoma * Uncontrolled bacterial, viral, or fungal infection (currently taking medication and with progression or no clinical improvement) * Prior malignancies except resected basal cell carcinoma or treated cervical carcinoma in situ; cancer treated with curative intent less than 5 years previously will not be allowed unless approved by the Medical Monitor or Protocol Chair; cancer treated with curative intent less than 5 years previously will be allowed * Pregnant (positive β-HCG) or breastfeeding; this patient population is excluded due to the lack of data on the use of Bexxar in patients who are pregnant or breastfeeding * Seropositivity for HIV; this patient population is excluded due to the lack of data on the use of Bexxar in HIV positive patients and because the treatment regimens are too immunosuppressive for this patient population * Fertile men or women unwilling to use contraceptive techniques from the time of initiation of mobilization until six-months post-transplant * Prior autologous or allogeneic hematopoietic stem cell transplantation (HSCT) * Patients with evidence of myelodysplastic syndrome/acute myeloid leukemia (MDS/AML) or abnormal cytogenetic analysis indicative of MDS on the pre-transplant bone marrow examination * Patients with a prior severe reaction to Rituxan or Filgrastim (G-CSF). Patients with severe reactions to G-CSF that receive pre-medication for control of the reaction are not excluded from study. * Patients who have received prior radioimmunotherapy * Patients with known hypersensitivity to murine proteins