Group Relative Policy Optimization (GRPO) relies on the diversity of $K$ rollouts within each group; otherwise, the group-mean advantage $A^{(k)} = r^{(k)} - μ_r$ collapses to zero. This presents a structural challenge for latent-reasoning models like Coconut, which feed continuous hidden states recurrently in place of discrete chain-of-thought tokens. Because the latent phase is inherently deterministic given the parameters and prompt, multiple rollouts produce identical trajectories, stalling GRPO's progress. Consequently, applying group-relative reinforcement learning to continuous latent reasoning has proven difficult. To address this, we propose sourcing the necessary stochasticity through structured dropout. By applying a single Bernoulli mask held constant across all latent recurrence steps for a given rollout, we generate essential trajectory variance. This shared mask effectively treats each rollout as a posterior sample from a variational distribution over parameters, allowing GRPO to optimize the expected reward of a Bayesian model-average policy. We provide both theoretical justification for this method -- including unbiasedness, variance reduction, and the well-definedness of the latent gradient -- and empirical validation. On GSM8K, dropout-GRPO improves a Coconut baseline from $27.29\%$ to $29.01\%$ pass@1, demonstrating the viability of GRPO learning for latent-reasoning models. Our work positions this as a practical, theoretically grounded approach for post-training latent-reasoning LLMs.