Edge-cloud collaborative inference is becoming a practical necessity for LLM-powered edge devices: on-device models often cannot afford the required reasoning capability, while cloud-only inference could be prohibitively costly and slow under strict latency and token/API budgets. However, existing edge-cloud collaboration methods often route per query or fixed steps simply based-on the estimated difficulty. Such coarse and static heuristics overlook subtask dependencies, missing opportunities for parallel execution and budget-adaptive routing. To this end, we propose \textbf{HybridFlow}, a resource-adaptive edge-cloud inference framework that (i) builds a dependency-aware DAG for each query and executes newly unlocked subtasks in parallel, reducing end-to-end latency; (ii) routes each subtask online to the edge or cloud via a learned benefit--cost utility model that dynamically trades accuracy gains against token/API and latency budgets, thereby reducing unnecessary cloud usage while preserving reasoning quality. Across GPQA, MMLU-Pro, AIME24, and LiveBench-Reasoning, HybridFlow improves the cost-accuracy trade-off, reducing latency and cloud API usage while maintaining competitive accuracy against strong structured reasoning baselines.

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