Inclusion Criteria:

          -  Participants must have histologically or cytologically confirmed diffuse large B-cell
             lymphoma (DLBCL), Ann Arbor stage IIX (bulky), III or IV. Participants with DLBCL
             transformed from follicular lymphoma (FL) or marginal zone lymphoma (MZL, including
             mucosa-associated lymphoid tissue [MALT] lymphomas), lymphoplasmacytic lymphoma (LPL),
             or nodular lymphocyte-predominant Hodgkin lymphoma (NLPHL) are eligible. Participants
             with grade IIIB follicular lymphoma (FL) and high-grade B-cell lymphomas with MYC and
             BCL2 and/or BCL6 rearrangements are also eligible. Participants with DLBCL that arose
             from prior chronic lymphocytic leukemia (CLL) (Richter's transformation) are not
             eligible

          -  As defined by the World Health Organization (WHO), eligible lymphoma subtypes include
             the following:

               -  DLBCL, not otherwise specified (NOS)

               -  DLBCL, germinal-center B-cell type (GCB)

               -  DLBCL, activated B-cell type (ABC)

               -  T-cell histiocyte-rich B-cell lymphomas (THRBCL)

               -  Primary cutaneous DLBCL, leg type

               -  Intravascular large B cell lymphoma

               -  EBV+ DLBCL, NOS

               -  DLBCL associated with chronic inflammation

               -  HHV8+ DLBCL, NOS

               -  High-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements

               -  High grade B-cell lymphoma, NOS

               -  Follicular lymphoma grade 3b

          -  Staging imaging must have occurred within 28 days prior to registration. Positron
             emission tomography (PET)-computed tomography (CT) baseline scans are strongly
             preferred; diagnostic quality magnetic resonance imaging (MRI), contrast-enhanced CT,
             or contrast-enhanced MRI scans are also acceptable if PET-CT is not feasible at
             baseline. Note: PET-CT will be required at end of treatment (EOT) and progression for
             response assessment. All measurable lesions must be assessed within 28 days prior to
             registration. Tests to assess non-measurable disease must be performed within 42 days
             prior to registration

          -  Participants with known human immunodeficiency virus (HIV)-infection are eligible
             providing they are on effective anti-retroviral therapy and have undetectable viral
             load at their most recent viral load test (must be within 26 weeks prior to
             registration). Participants with known HIV must have a CD4 count checked within 28
             days before starting therapy, but may proceed with therapy regardless of CD4 count

          -  All participants must be screened for chronic hepatitis B virus (HBV) within 28 days
             prior to registration. Participants with known HBV infection (positive serology) must
             also have a HBV viral load performed within 28 days prior to registration, and
             participants must have an undetectable HBV viral load on suppressive therapy within 28
             days prior to registration. Participants found to be HBV carriers during screening are
             eligible and must receive standard of care prophylaxis. Participants with active
             hepatitis B (HBV viral load > 500 IU/mL) within 28 days prior to registration are not
             eligible

          -  Participants with a known history of hepatitis C virus (HCV) infection must have an
             undetectable HCV viral load within in 28 days prior to registration

          -  Participants must have a Zubrod performance status of 0-2

          -  Participants must have adequate renal function, as demonstrated by a creatinine
             clearance, calculated by the Cockcroft and Gault formula, of >= 30 ml/min that was
             obtained within 28 days prior to registration

          -  Aspartate aminotransferase (AST) =< 2.5 x institutional upper limit of normal (IULN),
             alanine aminotransferase (ALT) =< 2.5 x IULN (within 28 days prior to registration)

          -  Total bilirubin =< 2 x institutional upper limit of normal (IULN), unless due to
             Gilbert's disease, hemolysis, or lymphomatous involvement of liver (within 28 days
             prior to registration). Note: If total bilirubin is elevated, and direct bilirubin is
             subsequently performed (within 28 days prior to registration) and resulted to be =< 2
             x IULN, the participant will be considered eligible

          -  Absolute neutrophil count (ANC) >= 1000/mcL (within 28 days prior to registration)

          -  Platelets >= 75,000/mcL (within 28 days prior to registration)

          -  If there is a documented lymphomatous involvement of the bone marrow, bone marrow
             function within 28 days prior to registration, as evidenced by:

               -  ANC >= 500/mcL

               -  Platelets >= 50,000/mcL

          -  Participants must have a left ventricular ejection (LVEF) fraction >= 45% as measured
             by echocardiogram or radionuclide (multigated acquisition scan [MUGA])
             ventriculography within 56 days prior to registration

          -  For the duration of the study treatment period and for at least 4 months following the
             last dose of study drug, male participants must agree to use effective contraceptive
             methods during sexual contact with a female of childbearing potential (FCBP) and must
             agree to refrain from semen or sperm donation during the same timeframe. Effective
             contraceptive methods include a history of vasectomy, use of hormonal contraception or
             an intrauterine device (IUD) by the female partner, or use of condoms

               -  A FCBP is a sexually mature woman who: 1) has not undergone a hysterectomy or
                  bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least
                  24 consecutive months (i.e., has had menses at any time in the preceding 24
                  consecutive months)

        Exclusion Criteria:

          -  Participants must not have known lymphomatous involvement of the central nervous
             system (CNS)

          -  Participants must not have active inflammatory bowel disease (such as, Crohn's
             disease, ulcerative colitis), celiac disease (i.e., sprue), prior gastrectomy or upper
             bowel removal, or any other gastrointestinal disorder or defect that would interfere
             with the absorption, distribution, metabolism, or excretion of the study drug and/or
             predispose the subject to an increased risk of gastrointestinal toxicity

          -  Participants must not have received any prior cytotoxic chemotherapy or rituximab for
             treatment of the newly diagnosed DLBCL. Participants who received a short course of
             glucocorticoids (=< 7 days) per the pre-phase are eligible. Inhaled, nasal, and
             topical steroid use is allowed. Prior cytotoxic chemotherapy and/or antibody therapy
             for an indolent lymphoma prior to transformation is allowed

          -  Participants must not have received more than a cumulative of 250 mg/m^2 of prior
             anthracycline therapy (at any time prior to registration)

          -  Participants must not currently be receiving any other investigational agents

          -  Participant must not have a history of allergic reactions attributed to azacitidine,
             mannitol, or other hypomethylating agents

          -  Participants must not have active infection (systemic fungal, bacterial, or viral
             infection) that is not controlled (defined as ongoing signs/symptoms related the
             infection without improvement despite appropriate antibiotics, antiviral therapy,
             and/or other treatment)

          -  Participants must not have active cardiac disease within 26 weeks prior to
             registration, including: symptomatic congestive heart failure (New York Heart
             Association [NYHA] class 4), unstable angina pectoris, hemodynamically unstable
             cardiac arrhythmia, or myocardial infarction

          -  Participants must not have >= grade 2 neuropathy, by Common Terminology Criteria for
             Adverse Events (CTCAE) version (v.) 5.0, within 28 days prior to registration

          -  Participants must not have any other known uncontrolled intercurrent illness
             including, but not limited to ongoing psychiatric illness/social situations that would
             limit compliance with study requirements