Speculative decoding accelerates LLM inference by drafting multiple tokens in parallel, with tree-based methods further improving efficiency through hierarchical structures. Dynamic-tree methods such as EAGLE-3 perform well under greedy decoding via deterministic top-K expansion and global pruning. However, in stochastic decoding (T>0), this mechanism collapses the draft distribution into one-hot probabilities, causing a severe drop in acceptance rate. This creates a dilemma: dynamic-tree methods sacrifice stochastic sampling to preserve context-aware topology, while static-tree methods preserve stochastic sampling with context-agnostic structures. The issue arises because the same probability distribution is used for two conflicting tasks: constructing the tree and verifying tokens. This coupling makes direct injection of randomness challenging due to the resulting stochastic process. We resolve this by decoupling these roles: RheoSampling assigns a token sampled from the draft distribution a proxy probability for tree expansion and pruning alongside its true sampling probability for verification. Specifically, we inject a sampled token among the deterministic top-K slots and treat it with different probabilities during construction and verification, making RheoSampling the first dynamic-tree method with both context-aware top-K construction and stochastic sampling while maintaining losslessness. We establish the lossless guarantee through an equivalence-class analysis that compresses the stochastic tree space into tractable classes. An OT-based verification strategy and a sparse draft mechanism ensure that theoretical gains translate into practical efficiency. Experiments across LLMs and benchmarks demonstrate improvements in acceptance rate and speedup over state-of-the-art dynamic tree methods. This framework may provide a template for analyzing stochastic tree structures.

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