Trajectory-Retrieval Speculative Decoding: When Does a Model's Own History Help?

Speculative decoding accelerates autoregressive language model inference by having a lightweight draft model propose multiple candidate tokens, which are then verified in parallel by a larger target model. However, after the first rejection, standard prefix-based verification discards the remaining draft suffix, so the computation spent generating and verifying those positions does not contribute to decoding progress. Focusing on DFlash, we show that rejected positions in a rejected suffix may still align with the target continuation, indicating that the draft model can retain useful semantic and structural information despite local token-level errors. Motivated by this observation and inspired by conditional diffusion, we introduce ReTrace, a rejected-trajectory conditioning method that conditions each draft block on the rejected suffix from the previous round rather than generating it from fresh mask placeholders alone. ReTrace retains the hidden representations of the rejected suffixes, aligns them with the next draft block, refines them using target-aware correction signals from the same verification pass, and admits them into the drafter's input embeddings through gated residual fusion. Because rejected tokens are never committed and target-side verification remains unchanged, ReTrace preserves the lossless property of speculative decoding without requiring an additional model forward pass. Experiments with Qwen3 models across mathematical reasoning, code generation, and open-ended dialogue demonstrate that ReTrace consistently improves average acceptance length and end-to-end decoding speed over its DFlash backbone. By introducing cross-round conditioning without modifying within-round proposal generation, ReTrace is largely orthogonal to existing drafting improvements and might be combined with them for further gains.

Speculative decoding accelerates generation by verifying multiple drafted tokens in a single target-model forward pass, reducing sequential decoding iterations. Model-free variants avoid auxiliary draft models by reusing text and model states already available during generation, but their speedup depends on the reliability of the constructed drafts. We identify two limitations of existing reuse-based methods: lexically anchored retrieval has limited recall under surface-form variation, and deterministic span copying can be brittle when the retrieved context does not uniquely determine the continuation. We propose \emph{AdaPLD}, a training-free method that adaptively improves both retrieval and draft construction. AdaPLD preserves high-precision lexical reuse while using semantic similarity to recover additional reuse opportunities when lexical matching fails. It further constructs branched reuse hypotheses to account for continuation uncertainty, rather than relying on a single copied span. Across diverse benchmarks, AdaPLD reduces target-model forward passes and achieves up to $3.10\times$ decoding speedup.

Speculative decoding accelerates large language model inference by using a low-cost draft model to propose tokens that the full-size target model verifies in parallel. Parallel and semi-autoregressive (semi- AR) drafters improve drafting efficiency by proposing an entire block in a single forward pass, but training them raises a new difficulty: the draft distribution for a given position depends on where the decoding round starts, and where rounds start depends on how many tokens earlier rounds accepted. Existing training objectives typically rely on block-local surrogates that ignore this cross-round coupling, and therefore do not directly optimize the global decoding efficiency. In this work, we develop a theoretical framework for training and evaluating these drafters by representing speculative decoding as a Markov reward process. This formulation yields the Expected Decoding Rounds (EDR) objective, which weights local rejection costs by state occupancies and exactly equals the expected number of decoding rounds. Unlike prior surrogate objectives, EDR introduces no auxiliary hyperparameters. We then derive an exact temporal-difference gradient that supports unbiased stochastic optimization from target-model rollouts. The same framework also yields an exact offline evaluator for round counts, enabling paired drafter comparisons on shared target rollouts without running speculative decoding. Finetuning two state-of-the- art drafters, DSpark and DFly, with EDR consistently improves mean accepted length and outperforms existing training objectives across nine benchmarks spanning math reasoning, code generation, and chat.