# Variational Speculative Decoding: Rethinking Draft Training from Token Likelihood to Sequence Acceptance

arXiv: https://arxiv.org/abs/2602.05774 · HTML: https://mlsanity.com/paper/2602.05774/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 32 of its 59 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 30 of 32)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Break the Sequential Dependency of LLM Inference Using Lookahead Decoding](https://mlsanity.com/paper/2402.02057/) (2024)
- [DistillSpec: Improving Speculative Decoding via Knowledge Distillation](https://mlsanity.com/paper/2310.08461/) (2023)
- [Speculative Decoding with Big Little Decoder](https://mlsanity.com/paper/2302.07863/) (2023)
- [Accelerating Transformer Inference for Translation via Parallel Decoding](https://mlsanity.com/paper/2305.10427/) (2023)
- [Hydra: Sequentially-Dependent Draft Heads for Medusa Decoding](https://mlsanity.com/paper/2402.05109/) (2024)
- [Sequoia: Scalable, Robust, and Hardware-aware Speculative Decoding](https://mlsanity.com/paper/2402.12374/) (2024)
- [Learning Harmonized Representations for Speculative Sampling](https://mlsanity.com/paper/2408.15766/) (2024)
- [SWIFT: On-the-Fly Self-Speculative Decoding for LLM Inference Acceleration](https://mlsanity.com/paper/2410.06916/) (2024)
- [Kangaroo: Lossless Self-Speculative Decoding via Double Early Exiting](https://mlsanity.com/paper/2404.18911/) (2024)
- [LANTERN: Accelerating Visual Autoregressive Models with Relaxed Speculative Decoding](https://mlsanity.com/paper/2410.03355/) (2024)
- [Ouroboros: Generating Longer Drafts Phrase by Phrase for Faster Speculative Decoding](https://mlsanity.com/paper/2402.13720/) (2024)
- [ViSpec: Accelerating Vision-Language Models with Vision-Aware Speculative Decoding](https://mlsanity.com/paper/2509.15235/) (2025)
- [GRIFFIN: Effective Token Alignment for Faster Speculative Decoding](https://mlsanity.com/paper/2502.11018/) (2025)
- [DREAM: Drafting with Refined Target Features and Entropy-Adaptive Cross-Attention Fusion for Multimodal Speculative Decoding](https://mlsanity.com/paper/2505.19201/) (2025)
- [Speculative Decoding Reimagined for Multimodal Large Language Models](https://mlsanity.com/paper/2505.14260/) (2025)
- [Bridging Draft Policy Misalignment: Group Tree Optimization for Speculative Decoding](https://mlsanity.com/paper/2509.22134/) (2025)
- [Speculative Jacobi-Denoising Decoding for Accelerating Autoregressive Text-to-image Generation](https://mlsanity.com/paper/2510.08994/) (2025)
- [HiViS: Hiding Visual Tokens from the Drafter for Speculative Decoding in Vision-Language Models](https://mlsanity.com/paper/2509.23928/) (2025)

## Built on by (most cited first, 2 of 2)

- [Spec-AUF: Accept-Until-Fail Training under Train-Inference Misalignment for Masked Block Drafters](https://mlsanity.com/paper/2607.01893/) (2026)
- [APEX: Speculate smarter, not deeper](https://mlsanity.com/paper/2610.07780/) (2026)

## Abstract (arXiv)

Speculative decoding accelerates inference for (M)LLMs, yet a training-decoding discrepancy persists: while existing methods optimize single greedy trajectories, decoding involves verifying and ranking multiple sampled draft paths. We propose Variational Speculative Decoding (VSD), formulating draft training as variational inference over latent proposals (draft paths). VSD maximizes the marginal probability of target-model acceptance, yielding an ELBO that promotes high-quality latent proposals while minimizing divergence from the target distribution. To enhance quality and reduce variance, we incorporate a path-level utility and optimize via an Expectation-Maximization procedure. The E-step draws Monte Carlo samples from an oracle-filtered posterior, while the M-step maximizes weighted likelihood using Adaptive Rejection Weighting (ARW) and Confidence-Aware Regularization (CAR). Theoretical analysis confirms that VSD increases expected acceptance length and speedup. Extensive experiments across LLMs and MLLMs show that VSD achieves up to a 9.6% speedup over EAGLE-3 and 7.9% over ViSpec, significantly improving decoding efficiency.