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Recent advances in deep learning have been providing non-intuitive solutions to various inverse problems in optics. At the intersection of machine learning and optics, diffractive networks merge wave-optics with deep learning to design task-specific elements to all-optically perform various tasks such as object classification and machine vision. Here, we present a diffractive network, which is used to shape an arbitrary broadband pulse into a desired optical waveform, forming a compact pulse engineering system. We experimentally demonstrate the synthesis of square pulses with different temporal-widths by manufacturing passive diffractive layers that collectively control both the spectral amplitude and the phase of an input terahertz pulse. Our results constitute the first demonstration of direct pulse shaping in terahertz spectrum, where a complex-valued spectral modulation function directly acts on terahertz frequencies. Furthermore, a Lego-like physical transfer learning approach is presented to illustrate pulse-width tunability by replacing part of an existing network with newly trained diffractive layers, demonstrating its modularity. This learning-based diffractive pulse engineering framework can find broad applications in e.g., communications, ultra-fast imaging and spectroscopy.