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Deep leaing has been transformative in many fields,motivating the emergence of various optical computing architectures.Diffractive optical network is a recently introduced optical computing framework that merges wave optics with deep-leaing methods to design optical neural networks.Diffraction-based all-optical object recognition systems,designed through this framework and fabricated by 3D printing,have been reported to recognize handwritten digits and fashion products,demonstrating all-optical inference and generalization to sub-classes of data.These previous diffractive approaches employed monochromatic coherent light as the illumination source.Here,we report a broadband diffractive optical neural network design that simultaneously processes a continuum of wavelengths generated by a temporally incoherent broadband source to all-optically perform a specific task leaed using deep leaing.We experimentally validated the success of this broadband diffractive neural network architecture by designing,fabricating and testing seven different multi-layer,diffractive optical systems that transform the optical wavefront generated by a broadband THz pulse to realize (1) a series of tuneable,single-passband and dual-passband spectral filters and (2) spatially controlled wavelength de-multiplexing.Merging the native or engineered dispersion of various material systems with a deep-leaing-based design strategy,broadband diffractive neural networks help us engineer the light-matter interaction in 3D,diverging from intuitive and analytical design methods to create taskspecific optical components that can all-optically perform deterministic tasks or statistical inference for optical machine leaing.