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Broadband spectral filters are highly sought-after in many integrated photonics applications such as ultra-broadband wavelength division multiplexing, multi-band spectroscopy, and broadband sensing. In this study, we present the design, simulation, and experimental demonstration of compact and ultra-broadband silicon photonic filters with adiabatic waveguides. We first develop an optimization algorithm for coupled adiabatic waveguide structures, and use it to design individual, single-cutoff spectral filters. These single-cutoff filters are 1x2 port devices that optimally separate a broadband signal into short-pass and long-pass outputs, within a specified device length. We control the power roll-off and extinction ratio in these filters using the adiabaticity parameter. Both outputs of the filters operate in transmission, making it possible to cascade multiple filters in different configurations. Taking advantage of this flexibility, we cascade two filters with different cutoff wavelengths on-chip, and experimentally demonstrate band-pass operation. The independent and flexible design of these band edges enables filters with bandwidths well over 100 nm. Experimentally, we demonstrate band-pass filters with passbands ranging from 6.4 nm up to 96.6 nm. Our devices achieve flat-band transmission in all three of the short-pass, band-pass, and long-pass outputs with less than 1.5 dB insertion loss and extinction ratios of over 15 dB. These ultra-broadband filters can enable new capabilities for multi-band integrated photonics in communications, spectroscopy, and sensing applications.