arXiv Computation and Language

Serial Depth of Adaptive Parallel Sampling: Lower Bounds and Schedules for Masked Diffusion Models

arXiv Computation and Language
Aug 27

Conditional Total Correlation and the Serial Depth of Adaptive Parallel Sampling

The paper introduces a new framework for adaptive parallel sampling of discrete vectors, where a deterministic policy reveals coordinates round‑by‑round based on previously observed values and samples the remaining coordinates from their exact conditional marginals. The authors prove an exact identity linking the forward Kullback‑Leibler divergence of any policy to the expected conditional total correlation accumulated during the sampling process, establishing conditional total correlation as the precise information cost of within‑round parallelism. Using this identity, they derive zero‑error schedules for finite‑order Markov chains, characterize the serial depth of Bernoulli walks, and demonstrate separations between different reveal orders, permutation strategies, and string structures, thereby revealing how conditional dependence governs parallelizability. whyItMatters":"The results provide a principled, information‑theoretic measure of parallel sampling efficiency that can guide the design of decoding rules for masked diffusion models and other generative systems."

By Chuling Wen, Weijie Liang, Jian Lu
arXiv Machine Learning
Oct 16

Score Mismatch and Set-Constrained Sampling in Zero-Shot Conditional Discrete Diffusion

The paper presents a theoretical analysis of score mismatch in discrete diffusion models, deriving a KL divergence upper bound that quantifies the bias introduced when the training and target distributions differ. It examines partial-observation constraints such as text infilling and sentence completion, showing that the Conditional SEDD sampler can incur a bias that grows with dimension, vocabulary size, and compatibility. To mitigate this, the authors propose a Randomized Hard Clamping (RHC) sampler for coordinatewise set constraints, demonstrating through experiments that it effectively reduces bias and improves sampling performance.

By Renxiang Huang, Yuchen Liang, Yingbin Liang, Ness Shroff, Lifeng Lai
arXiv Machine Learning
Oct 8

Training Parallel Speculative Draft Models by Directly Minimizing Expected Decoding Rounds

The paper introduces the Expected Decoding Rounds (EDR) objective, a theoretical framework that models speculative decoding as a Markov reward process and directly optimizes the number of decoding rounds. EDR weights local rejection costs by state occupancies, eliminating auxiliary hyperparameters and enabling unbiased stochastic optimization via temporal‑difference gradients. Applying EDR to fine‑tune state‑of‑the‑art draft models (DSpark and DFly) improves mean accepted length and outperforms prior training objectives across nine benchmarks in math reasoning, code generation, and chat.

By Yunxiao Zhao, Changxiao Cai
arXiv Machine Learning
Oct 2

Fork-dLLM: Avoiding the Flexibility Trap in Diffusion Language Models

The paper introduces Fork-dLLM, a hybrid sampling strategy for diffusion language models that combines parallel token generation with autoregressive ordering only at uncertain fallback steps, thereby avoiding the flexibility trap that reduces generation diversity. It also presents ForkGRPO, an extension that applies the GRPO objective selectively during post‑training rollouts, preserving policy‑likelihood ratios while cutting rollout and optimization costs. Experiments show Fork-dLLM achieves pass@k scaling comparable to autoregressive sampling but 2–3× more efficient, and ForkGRPO matches or surpasses AR‑based GRPO baselines at significantly lower training expense.

By Stipe Frkovi\'c, Metod Jazbec, Christian A. Naesseth
arXiv Machine Learning
Oct 16

Query-Efficient Rejection Sampling for Parallel Masked Diffusion

The paper introduces the Single-Increment Rejection Sampler (SIRS) to improve query efficiency in parallel masked diffusion models (MDMs). SIRS estimates the log acceptance probability using only one randomly sampled increment, then applies a Bernoulli factory to decide accept/reject outcomes. By Rao‑Blackwellizing each increment and bounding the KL‑divergence, SIRS reduces bias while maintaining parallel decoding performance.

By Shiyuan Zhang, Xuheng Li, Qiwei Di, Quanquan Gu
arXiv AI
Aug 3

Predict-then-Diffuse: Adaptive Response Length for Compute-Budgeted Inference in Diffusion LLMs

arXiv:2605. 04215v3 Announce Type: replace-cross Abstract: Diffusion-based Large Language Models (D-LLMs) represent a promising frontier in generative AI, offering fully parallel token generation that can lead to significant throughput advantages and superior GPU utilization over the traditional autoregressive paradigm.

By Michael Rottoli, Subhankar Roy, Stefano Paraboschi