A Study of Polatuzumab Vedotin (DCDS4501A) in Combination With Rituximab or Obinutuzumab Plus Bendamustine in Participants With Relapsed or Refractory Follicular or Diffuse Large B-Cell Lymphoma

Inclusion Criteria:

* Histologically confirmed relapsed or refractory FL (Grades 1, 2, or 3a) or relapsed or refractory DLBCL
* If the participant has received prior bendamustine, response duration must have been greater than (\>) 1 year (for participants who have relapse disease after a prior regimen)
* At least one bi-dimensionally measurable lesion on imaging scan defined as \>1.5 centimeters (cm) in its longest dimension
* Confirmed availability of archival or freshly collected tumor tissue
* The Phase II NF Cohorts (Arms G and H) will be required to submit tissue and pathology report for central pathology review.
* Life expectancy of at least 24 weeks
* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2
* Adequate hematological function unless inadequate function is due to underlying disease

Exclusion Criteria:

* History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibodies (MAbs, or recombinant antibody-related fusion proteins) or known sensitivity or allergy to murine products
* Contraindication to bendamustine, rituximab, or obinutuzumab
* Prior use of any MAb, radioimmunoconjugate, or antibody-drug conjugate (ADC) within 4 weeks or 5 half-lives before Cycle 1 Day 1
* Treatment with radiotherapy, chemotherapy, immunotherapy, immunosuppressive therapy, or any investigational agent for the purposes of treating cancer within 2 weeks prior to Cycle 1 Day 1
* Ongoing corticosteroid use \>30 mg per day prednisone or equivalent, for purposes other than lymphoma symptom control
* Completion of autologous stem cell transplant (SCT) within 100 days prior to Cycle 1 Day 1
* Prior allogeneic SCT
* Eligibility for autologous SCT
* Grade 3b FL
* History of transformation of indolent disease to DLBCL
* Primary or secondary CNS lymphoma
* Current Grade \>1 peripheral neuropathy
* Evidence of significant, uncontrolled concomitant diseases that could affect compliance with the protocol or interpretation of results, including significant cardiovascular disease (such as New York Heart Association Class III or IV cardiac disease, myocardial infarction within the last 6 months, unstable arrhythmias, or unstable angina) or significant pulmonary disease (including obstructive pulmonary disease and history of bronchospasm)
* Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment or any major episode of infection requiring treatment with IV antibiotics or hospitalization within 4 weeks prior to Cycle 1 Day 1
* Suspected or latent tuberculosis
* Positive test results for chronic hepatitis B virus (HBV) infection or for hepatitis C virus (HCV) antibody
* Known history of human immunodeficiency virus (HIV) seropositive status or known infection with human T-cell leukemia virus 1 (HTLV-1) virus
* Women who are pregnant or lactating or who intend to become pregnant within a year of the last dose of study treatment in the rituximab cohort or within 18 months of last dose in the obinutuzumab cohort
* Evidence of laboratory abnormalities in standard renal, hepatic, or coagulation function tests
* Treatment with chimeric antigen receptor T-cell therapy within 100 days prior to Cycle 1, Day 1