A Study of Polatuzumab Vedotin in Combination With Rituximab or Obinutuzumab, Cyclophosphamide, Doxorubicin, and Prednisone in Participants With B-Cell Non-Hodgkin's Lymphoma

Inclusion Criteria:

All Participants:

* At least one bi-dimensionally measurable lesion, defined as greater than (\>) 1.5 centimeters (cm) in its longest dimension
* Life expectancy of at least 24 weeks
* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2
* Adequate hematologic function (unless inadequate function is due to underlying disease, as established by extensive bone marrow involvement or is due to hypersplenism secondary to the involvement of the spleen by lymphoma per the investigator)
* Agreement to use highly effective contraception measures. Women of childbearing potential must agree to remain abstinent or use contraceptive measures that result in a failure rate of \<1 percent (%) per year during the treatment period and for at least 12 months for R-CHP arm or for at least 18 months for G-CHP arm after the last dose of study drug. Men must agree to remain abstinent or to use a condom plus an additional contraceptive method that together result in a failure rate of \<1% per year during the treatment period and for at least 5 months after the last dose of study drug

Dose-Escalation Portion of the Study:

* Histologically confirmed B-cell NHL: Participants with newly diagnosed B-cell NHL or relapsed/refractory B-cell NHL are eligible
* No more than one prior systemic treatment regimen for B-cell NHL (single agent anti-cluster of differentiation \[CD\] 20 monoclonal antibody therapy will not be counted as a prior treatment regimen)
* No prior treatment with anthracyclines

Expansion Portion of the Study:

* Previously untreated participants with diffuse large B-cell lymphoma (DLBCL)
* International Prognostic Index (IPI) score of 2-5

Exclusion Criteria:

Dose-Escalation Portion of the Study:

* Diagnosis of primary mediastinal DLBCL

Expansion Portion of the Study:

* Participants with transformed lymphoma
* Prior therapy for NHL

All Participants:

* Prior stem cell transplant
* History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibodies or known sensitivity or allergy to murine products
* Contraindication to receive any of the individual components of R-CHP or G-CHP
* Current Grade greater than (\>) 1 peripheral neuropathy
* Ongoing corticosteroid use of \>30 milligrams per day (mg/day) of prednisone/prednisolone or equivalent. Participants receiving corticosteroid treatment with less than or equal to (\</=) 30 mg/day of prednisone/prednisolone or equivalent must be documented to be on a stable dose of at least 4 weeks' duration before Cycle 1 Day 1
* Primary central nervous system (CNS) lymphoma
* Vaccination with live vaccines within 6 months before Cycle 1 Day 1
* History of other malignancy that could affect compliance with the protocol or interpretation of results. Participants with a history of curatively treated basal or squamous cell carcinoma or melanoma of the skin or in situ carcinoma of the cervix are eligible. Participants with a malignancy that has been treated with surgery alone with curative intent will also be excluded unless the malignancy has been in documented remission without treatment for greater than or equal to (\</=) 5 years before enrollment
* Evidence of significant, uncontrolled concomitant diseases, including renal disease that would preclude chemotherapy administration, or pulmonary disease (including obstructive pulmonary disease and history of bronchospasm)
* Significant cardiovascular disease (such as New York Heart Association Class III or IV cardiac disease, congestive heart failure, myocardial infarction within the previous 6 months, unstable arrhythmias, or unstable angina) or significant pulmonary disease
* 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 (relating to the completion of the course of antibiotics) within 4 weeks before Cycle 1 Day 1
* Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis
* Positive for hepatitis B or hepatitis C infection
* Prior radiotherapy to the mediastinal/pericardial region
* Pregnant or lactating women
* Recent major surgery within 6 weeks before the start of Cycle 1 Day 1