Snapshot ultrafast optical imaging (SUOI) plays a vital role in capturing complex transient events in real time, with significant implications for both fundamental science and practical applications. As an outstanding talent in SUOI, compressed ultrafast photography (CUP) has demonstrated remarkable frame rate reaching trillions of frames per second and hundreds of sequence depth. Nevertheless, as CUP relies on streak cameras, the system's imaging fidelity suffers from an inevitable limitation induced by the charge coupling artifacts in a streak camera. Moreover, although advanced image reconstruction algorithms have improved the recovered scenes, its high compression ratio still causes a compromise in image quality. To address these challenges, we propose a novel approach termed all-optical discrete illumination compressed ultrafast photography (AOD-CUP), which employs a free-space angular-chirp-enhanced delay (FACED) technique to temporally stretch femtosecond pulses and achieves discrete illumination for dynamic scenes. With its distinctive system architecture, AOD-CUP features adjustable frame numbers and flexible inter-frame intervals ranging from picoseconds to nanoseconds, thereby achieving high-fidelity ultrafast imaging in a snapshot. Experimental results demonstrate the system's superior dynamic spatial resolution and its capability to visualize ultrafast phenomena with complex spatial details, such as stress wave propagation in LiF crystals and air plasma channel formation. These results highlight the potential of AOD-CUP for high-fidelity, real-time ultrafast imaging, which provides an unprecedented tool for advancing the frontiers of ultrafast science.