This is a Phase 2 trial evaluating the efficacy of adding the combination of GaRD x 2 cycles following 3 cycles of the standard salvage regimen of RICE for the treatment of relapsed or refractory diffuse, large B-cell lymphoma (DLBCL). The study will include patients who have relapsed after 1 prior treatment regimen or who are refractory to initial chemotherapy. We will evaluate patients for response rate (both partial and complete), toxicities, as well as overall and progression free survival. Eligible patients will receive standard RICE x 3 cycles followed by GaRD x 2 cycles. Patients who would otherwise be eligible, may then proceed to autologous stem cell transplant (ASCT).