Full waveform inversion (FWI) stands as the forefront geophysical inversion approach, however, its impediment in practical applications persists due to the absence of prior information and limitations in data acquisition. Addressing this challenge, we introduce implicit FWI (IFWI) which represents subsurface models as continuous and implicit functions, thereby reducing dependency on the initial model with frequency principle in deep learning optimization. Furthermore, through the design of a specialized deep learning model that emphasizes rigorous low-frequency learning, we present a robust IFWI algorithm exhibiting high-resolution reconstruction capabilities, even when low-frequency information is absent in observations, as demonstrated in numerical experiments. Moreover, experimental findings underscore the heightened robustness, reduced data requirements, and strong generalization ability of the proposed robust IFWI algorithm. This highlights its applicability to a variety of subsurface models with diverse acquisition settings, indicating promising potential for practical seismic inversion.