Speculative decoding accelerates large language model inference by using smaller draft models to generate candidate tokens for parallel verification. However, current approaches are limited by sequential stage dependencies that prevent full hardware utilization. We present PipeSpec, a framework that generalizes speculative decoding to use multiple models arranged in a hierarchical pipeline, enabling asynchronous execution with lightweight coordination for prediction verification and rollback. Our analytical model characterizes token generation rates across pipeline stages and proves guaranteed throughput improvements over traditional decoding for any non-zero acceptance rate. We further derive closed-form expressions for steady-state verification probabilities that explain the empirical benefits of pipeline depth. We validate PipeSpec across text summarization, mathematical reasoning, and code generation tasks using LLaMA 2 and 3 models, demonstrating that pipeline efficiency increases with model depth, providing a scalable approach to accelerating LLM inference on multi-device systems. Our code is available at https://github.com/BradMcDanel/PipeSpec.

Sequential dependencies present a fundamental bottleneck in deploying large-scale autoregressive models, particularly for real-time applications. While traditional optimization approaches like pruning and quantization often compromise model quality, recent advances in generation-refinement frameworks demonstrate that this trade-off can be significantly mitigated.This survey presents a comprehensive taxonomy of generation-refinement frameworks, analyzing methods across autoregressive sequence tasks. We categorize methods based on their generation strategies (from simple n-gram prediction to sophisticated draft models) and refinement mechanisms (including single-pass verification and iterative approaches). Through systematic analysis of both algorithmic innovations and system-level implementations, we examine deployment strategies across computing environments and explore applications spanning text, images, and speech generation. This systematic examination of both theoretical frameworks and practical implementations provides a foundation for future research in efficient autoregressive decoding. In the appendix A, we additionally provide experimental comparisons of various baseline methods.