Abstract Water vapor concentration in turbulent clouds fluctuates over a wide range of scales, challenging physical understanding of droplet growth mechanisms, prediction of droplet size distributions, and attribution of causal connections. We generalize a minimalist Brownian‐motion model (McGraw & Liu, 2006, https://doi.org/10.1029/2005gl023545), valid only under strongly damped fluctuations, to a coupled stochastic system where the saturation ratio follows an Ornstein‐Uhlenbeck process. A memory parameter spans the full correlation continuum, recovering the previous model as a limiting case. We further incorporate an information‐flow framework to quantify the direction and strength of causal influences between the saturation ratio and droplet growth. Simulations confirm theoretical predictions and show that (a) spectral broadening depends on correlation time and standard deviation of saturation ratio fluctuations and (b) causal coupling between the saturation ratio and droplet size weakens as the size distribution broadens.