The rapidly evolving field of generative artificial intelligence technology has introduced innovative approaches for developing semantic communication (SemCom) frameworks, leading to the emergence of a new paradigm-generative SemCom (GSC). However, the complex processes involved in semantic extraction and generative inference may result in considerable latency in resource-constrained scenarios. To tackle these issues, we introduce a new GSC framework that involves fast and adaptive semantic transmission (FAST-GSC). This framework incorporates one innovative communication mechanism and two enhancement strategies at the transmitter and receiver, respectively. Aiming to reduce task latency, our communication mechanism enables fast semantic transmission by parallelizing the processes of semantic extraction at the transmitter and inference at the receiver. Preliminary evaluations indicate that while this mechanism effectively reduces task latency, it could potentially compromise task performance. To address this issue, we propose two additional methods for enhancement. First, at the transmitter, we employ reinforcement learning to discern the intrinsic temporal dependencies among the semantic units and design their extraction and transmission sequence accordingly. Second, at the receiver, we design a semantic difference calculation module and propose a sequential conditional denoising approach to alleviate the stringent immediacy requirement for the reception of semantic features. Extensive experiments demonstrate that our proposed architecture achieves a performance score comparable to the conventional GSC architecture while realizing a 52% reduction in residual task latency that extends beyond the fixed inference duration.