The purpose of this trial is to find out if epcoritamab, also known as EPKINLY™ and GEN3013, is safe and works well as treatment for participants with DLBCL that are not responding to treatment, have grown in size, or have come back following treatment with at least 1 prior systemic cancer therapy. All participants in this trial will be randomly assigned to receive either epcoritamab or a pre-specified investigator's choice (standard of care) chemotherapy (either rituximab + gemcitabine + oxaliplatin \[R-GemOx\], or bendamustine + rituximab \[BR\]). Participants must have failed or be ineligible to receive an autologous stem cell transplant (ASCT). Epcoritamab will be injected under the skin. Investigator's choice chemotherapy will be given intravenously. Trial details include: * The trial duration will be up to 5 years after last participant is randomized. * All trial participants have a 21-day screening period, a treatment period, and a follow-up period that continues until death. * The estimated trial duration for an individual participant depends upon the treatment arm assigned: * Participants who receive epcoritamab will have 28-day treatment cycles. Epcoritamab will be given once weekly for the first 3 months, then every other week for 6 months, then every 28 days until lymphoma progression or unacceptable adverse events. * Participants who receive investigator's choice (standard of care) chemotherapy will receive treatments either: * R-GemOx: On Day 1 (or Day 1 \& Day 2), and Day 15 (or Day 15 \& Day 16) every 28 days, for up to 4 months; or * BR: On Day 1 and Day 2 every 3 weeks for up to 4.5 months.