Inclusion Criteria for Phase Ib and Phase II Portions

          -  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

          -  Eastern Cooperative Oncology Group Performance Status of 0, 1, or 2

          -  Adequate hematologic function

        Inclusion Criteria for Phase Ib Portion

        Participants must also meet the following criteria for study entry into the Phase Ib
        portion:

          -  Histologically confirmed B-cell NHL according to the World Health Organization (WHO)
             2016 classification expected to express the cluster of differentiation-20 (CD20)
             antigen

          -  Relapsed or refractory (R/R) B-cell NHL after at least one prior systemic lymphoma
             therapy

          -  Treatment with at least one prior CD20-directed therapy

          -  Group B only: no prior treatment with polatuzumab vedotin

        Inclusion Criteria for Phase II Portion

        Participants must also meet the following criteria for study entry in the Phase II portion:

          -  Previously untreated, histologically confirmed DLBCL according to WHO 2016
             classification

          -  International Prognostic Index (IPI) score of 2-5

        Exclusion Criteria

          -  Prior treatment with mosunetuzumab

          -  Prior allogenic stem-cell transplant

          -  Current Grade >1 peripheral neuropathy

          -  Participants with 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)

          -  Prior solid organ transplantation

          -  History of autoimmune disease

          -  Current or past history of central nervous system (CNS) lymphoma

          -  Current or past history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or
             neurodegenerative disease

          -  Significant cardiovascular disease or pulmonary disease

          -  Clinically significant history of liver disease

          -  Recent major surgery within 4 weeks before the start of C1D1, other than superficial
             lymph node biopsies for diagnosis

        Exclusion Criteria for Phase Ib Portion

        Participants who also meet any of the following criteria will be excluded from study entry
        in the Phase Ib portion:

          -  Prior treatment with chemotherapy, immunotherapy, and biologic therapy 4 weeks prior
             to C1D1

          -  Prior treatment with radiotherapy within 2 weeks prior to C1D1

          -  Adverse events from prior anti-cancer therapy resolved to ≤Grade 1 (with the exception
             of alopecia and anorexia)

          -  Prior treatment with >250 mg/m^2 doxorubicin (or equivalent anthracycline dose)

        Exclusion Criteria for Phase II Portion

        Participants who also meet any of the following criteria will be excluded from study entry
        in the Phase II portion:

          -  Participants with transformed lymphoma

          -  Prior therapy for B-cell NHL