Fresnel incoherent correlation holography (FINCH) is traditionally implemented using liquid-crystal spatial light modulators, whereas implementation using digital micromirror devices (DMDs) remains challenging, because binary phase-encoding approaches cannot accurately reproduce the wavefronts required for high-fidelity hologram synthesis. We present LEAF-FINCH, a learning-based binary mask design framework that directly optimizes DMD masks using Rayleigh–Sommerfeld wave propagation. LEAF-FINCH achieves approximately a 1.4-fold improvement in SSIM for the biological specimen and a 1.1-fold improvement for the resolution target compared with the Lee-phase implementation.