This study will evaluate the safety, pharmacokinetics, and preliminary efficacy of
      mosunetuzumab following first-line diffuse large B-cell lymphoma (DLBCL) immunochemotherapy
      in participants with a best response of stable disease or partial response, or in
      elderly/unfit participants with previously untreated DLBCL, or subcutaneous mosunetuzumab in
      combination with polatuzumab vedotin IV in elderly/unfit participants with previously
      untreated DLBCL.
    
        Inclusion Criteria for All Cohorts
          -  At least one bi-dimensionally measurable nodal lesion, defined as > 1.5 cm in its
             longest dimension, or one bi-dimensionally measurable extranodal lesion, defined as >
             1.0 cm in its longest diameter
          -  Adequate hematologic function
          -  Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2; with the
             exception of South Korea, where participants 80 years or older with ECOG >/= 2 will
             not be eligible
        Inclusion Criteria Specific to Cohort A
        Participants in Cohort A must also meet the following criteria for study entry:
          -  Histologically confirmed DLBCL according to World Health Organization (WHO) 2016
             expected to express the cluster of differentiation-20 (CD20) antigen
          -  One prior therapy with any systemic anthracycline-based chemoimmunotherapy containing
             regimen for previously untreated DLBCL
          -  Best response of SD or PR to prior systemic chemoimmunotherapy at the end of induction
             treatment in accordance with the Lugano 2014 criteria
        Inclusion Criteria Specific to Cohorts B and C
        Participants in Cohorts B and C must also meet the following criteria for study entry:
          -  Previously untreated, histologically confirmed, DLBCL according to WHO 2016
             classification
          -  Age >/= 80 years, or
          -  Age 65-79 years and considered ineligible for chemoimmuotherapy (R-CHOP) with at least
             one of the following: Impairment in at least two activity of daily living (ADL)
             components as defined in the protocol; impairment in at least two instrumental ADL
             components as defined in the protocol; cumulative illness rating scale - geriactic
             (CIRS-G) score of at least one cormorbidity with a severity score of 3-4 or a score of
             2 in >/= 8 comorbidities; impairment in cardiac function, renal function, liver
             function, or other comorbidities such that the participant is unfit for full-dose
             immunochemotherapy, such as rituximab plus cyclophosphamide, doxorubicin, vincristine,
             and prednisone (R-CHOP)
          -  Participants with an initial ECOG performance status of 3 may be considered during
             screening if the performance status is DLBCL-related and if pre-phase treatment during
             the screening phase (not more than 100 mg/day up to 7 days prior to Cycle 1 Day 1)
             results in an improvement of ECOG performance status to </= 2 prior to enrollment
        Exclusion Criteria for All Cohorts
        Participants who meet any of the following criteria will be excluded from study entry:
          -  Transformed lymphoma
          -  CNS lymphoma
          -  Prior treatment with mosunetuzumab
          -  Prior stem cell transplant (autologous and allogeneic)
          -  History of confirmed progressive multifocal leukoencephalopathy (PML)
          -  Known or suspected chronic active Epstein Barr virus (CAEBV), hepatitis B, hepatitis C
             (HCV), or Human Immunodeficiency Virus (HIV)
          -  Known or suspected history of hemophagocytic lymphohistiocytosis (HLH)
          -  Prior solid organ transplantation
          -  Current or past history of central nervous system (CNS) disease, such as stroke,
             epilepsy, CNS vasculitis, or neurodegenerative disease
          -  Clinically significant history of liver disease
          -  Prior treatment with radiotherapy within 2 weeks prior to Cycle 1, Day 1 (C1D1)
          -  Significant cardiovascular disease
        Exclusion Criteria Specific to Cohort A
        Participants in Cohort A who meet the following criteria will be excluded from study entry:
        - Prior treatment with chemotherapy, immunotherapy, or biologic therapy 4 weeks prior to
        C1D1
        Exclusion Criterion Specific to Cohorts B and C
        Participants in Cohorts B and C who meet the following criterion will be excluded from
        study entry:
        - Prior treatment for DLBCL with chemotherapy, immunotherapy, and biologic therapy
        Exclusion Criteria Specific to Cohort C
        Participants in Cohort C who meet the following criteria will be excluded from study entry:
        - Current Grade >1 peripheral neuropathy by clinical examination or demyelinating form of
        Charcot-Marie-Tooth disease