Chalcogenide fibers have attracted much attention for multi-octave spanning supercontinuum generation in the mid-infrared range. However, readily optimizing the dispersion characteristics as well as other mode properties is still problematic because it is difficult to fabricate chalcogenide fibers with sophisticated structures. In this work, we numerically investigate the liquid infiltration as a post-processing method to optimize the dispersion shapes, so that the nonlinear dynamics and spectro-temporal properties of supercontinuum generation are efficiently controlled. In particular, water, carbon disulfide (CS2), carbon tetrachloride (CCl4), and bromoform (CHBr3) are selected to fill into all cladding air holes of As38Se62 fibers for dispersion engineering. By pumping a femtosecond laser at 4.5 μm, pulse duration of 250 fs, and pulse energy of 0.1 nJ (peak power of 0.4 kW), the unfilled and CCl4-filled fibers provide soliton-induced supercontinuum generation with a spectral bandwidth of 2.5–6.5 μm and 2.0–5.5 μm, respectively. Whilst, CHBr3-filled fiber offers all-normal dispersion supercontinuum generation with high coherence and spectral bandwidth of 2.2–5.2 μm. In contrast, unfortunately, CS2 and water-filled fibers have complex dispersion shapes and provide narrow bandwidth supercontinua. We also thoroughly numerically investigate the tapered fibers, which assure both high coupling efficiency with laser sources and high nonlinearity, for broad mid-infrared supercontinuum generation. The results point out that liquid-filled tapered fibers can provide both anomalous and all-normal dispersion SC generation with an octave-spanning bandwidth via the same value of input peak power (0.4 kW). With a large core diameter (12 μm) at the input and output fiber ends, the tapered fibers have a potential to couple with high-power laser pulses without fiber damage, therefore, they can provide supercontinuum spectra with broad bandwidth and high spectral power density for practical applications in sensing, gas detection, and LIDAR.