Reef-building corals are inherently sessile organisms. However, motion is an important behavioral trait of coral polyps, which plays an essential role in feeding, competition, defense, reproduction, and thus, survival and fitness. Notwithstanding the importance of inherent temporal and spatial multiscale features of polyps, their quantitative properties and modeling still remain challenging and unexplored. Here, we observe Pocillopora acuta in vivo under different light and temperature conditions using a fluidic platform that allows the direct microscopic study of small live coral fragments, where the stochastic dynamics of the in-plane waving motion of polyps is uncovered. The relationship between polyps on nubbins is described by motion-correlation analysis. Additionally, the fractional Brownian motions of polyps under certain light conditions and temperatures are revealed by the Hurst index via power spectral analysis. Finally, the motion of polyps is modeled by Langevin dynamics, numerically obtained by data-driven parameterization. This combination of experimental observations, numerical analysis, and theoretical modeling opens an avenue to boost our understanding of the biological and physical behaviors of corals in relation to changing environmental conditions.