Lensless imaging is an approach to microscopy in which a high-resolution image of an object is reconstructed from one or more measured diffraction patterns, providing a solution in situations where the use of imaging optics is not possible. However, current lensless imaging methods are typically limited by the need for a light source with a narrow, stable and accurately known spectrum. We have developed a general approach to lensless imaging without spectral bandwidth limitations or sample requirements. We use two time-delayed coherent light pulses and show that scanning the pulse-to-pulse time delay allows the reconstruction of diffraction-limited images for all the spectral components in the pulse. In addition, we introduce an iterative phase retrieval algorithm that uses these spectrally resolved Fresnel diffraction patterns to obtain high-resolution images of complex extended objects. We demonstrate this two-pulse imaging method with octave-spanning visible light sources, in both transmission and reflection geometries, and with broadband extreme-ultraviolet radiation from a high-harmonic generation source. Our approach enables effective use of low-flux ultra-broadband sources, such as table-top high-harmonic generation systems, for high-resolution imaging. © 2014 CIOMP. All rights reserved.