Abstract: Edge applications increasingly combine CNN-based perception with edge-deployable Transformer-based language models, but deploying such heterogeneous workloads on resource-constrained devices is challenging because inference latency varies with both input difficulty and runtime hardware state. Early-exit inference reduces computation by terminating at intermediate stages, yet existing methods are often model-specific and rely on static latency profiles that become stale under dynamic edge conditions. This paper presents UniExit, a unified latency-aware early-exit runtime for heterogeneous edge AI. UniExit abstracts CNN blocks and Transformer layers as ordered stages and applies a common latency-aware routing policy while retaining model-specific quality mechanisms. It predicts the cost of reaching the next exit from runtime state and inference progress to make budget-aware continue-or-exit decisions. UniExit combines runtime-state-aware latency prediction, cache-based prediction reuse, trend-aware fallback, and CNN-specific exit stabilization to provide low-overhead and robust online control. We implement UniExit on multiple edge and edge-cloud platforms and evaluate it with representative CNN and Transformer-based language-model workloads. Across single-workload, concurrent heterogeneous, and edge-cloud settings, UniExit consistently improves deadline satisfaction and latency-accuracy trade-offs over existing progressive inference baselines, while reducing redundant exit-module computation and task-level energy consumption.