Channel networks across fluvial landscapes are believed to have evolved to minimize energy expenditure[1–3], as evidenced by the similarities between computer-generated optimal channel networks (OCNs) and real networks[4,5]. However, the specific mechanisms driving energy minimization in fluvial landscapes remain largely elusive[6]. Here we propose that randomness has a profound role in landscape evolution[7] and that efficient channel networks emerge when the probability of a channel pixel changing its flow direction decreases with drainage area. The proposed probabilistic growth model then employs a power function to simulate channel-network evolution, with positive exponent (𝜂) values leading to asymptotic decrease of energy expenditure. An interpretation of this result is energy minimization tendency of river networks is a result of landscape evolution following specific adaptive rules rather than being the cause of landscape evolution itself. A greater 𝜂 ensures a greater restriction on the role of randomness and thus results in a more stable channel network configuration, and vice versa. Interestingly, the most efficient networks are observed to emerge always at 𝜂 =0.5, suggesting that randomness plays an important but limited role in the emergence of efficient channel networks. The proposed framework holds promise for explaining the evolution of other tree-like networks in nature and for developing more efficient optimization methods for practical applications.